From Ask Dr. Math, a Forum special outreach project (high school collection)
- Partitioning the Integers (Boehmk) 3/15/95
One of my students chose the topic of partitions of the positive integers....
From Ask Dr. Math, a Forum special outreach project (middle school collection)
- Combinations of Coins (Stewart) 1/28/96
If I had 6 coins in my pocket, how many combinations could I have?
From Ask Dr. Math, a Forum special outreach project (high school collection)
- Lines determined by 5 points (Fass) 11/13/94
How many lines are determined by 5 points, no three of which are collinear?
From Ask Dr. Math, a Forum special outreach project (high school collection)
- Five Noncollinear Points (Gomez) 4/2/95
In general, how many undirected lines and how many circles are determined by five noncollinear points?
From Ask Dr. Math, a Forum special outreach project (middle school collection)
- What Color Hat am I Wearing? (Yu) 4/17/96
Three students close their eyes, and the teacher puts a hat on each of their heads (hiding the other two hats)...
From Ask Dr. Math, a Forum special outreach project (high school collection)
- Number of Combinations for 7 Dice (Bertler) 2/22/95
I'm looking for the derived formula solution for the following problem someone posted in a math echo: There are seven dice. Each die has six faces. How many different combinations are there of these seven dice?
From Ask Dr. Math, a Forum special outreach project (high school collection)
- Permutation Formula (Grech) 4/23/95
I can't for the life of me remember the formula for calculating the total possible number of ways to choose 'r' objects out of a total 'n' objects.
From Ask Dr. Math, a Forum special outreach project (high school collection)
- Permutations of Lottery Numbers (RNJM1) 8/5/95
Our new lotto will start soon and the object is to pick 5 numbers, 1 through 39. No repeat or bonus numbers. How can I get a listing of all 575,000+ possible numbers?
From Ask Dr. Math, a Forum special outreach project (high school collection)
- Winning the UK National Lottery (Dominic) 11/8/95
I need to know the odds on the UK National Lottery: punters choose 6 different numbers between 1 and 49. How many permutations? How can I calculate the reduced number of permutations to reflect the fact that the order of the chosen numbers is not relevant?
From Ask Dr. Math, a Forum special outreach project (high school collection)
- Combinations for Casting a Play (Pennell) 11/15/95
Here's a list of people trying out for parts in the school play. If someone does not get a part he or she may try out for another. How many possible casts are there?
From Ask Dr. Math, a Forum special outreach project (high school collection)
- Combinations of Images on a TV Screen (Kent) 12/6/95
I'd like to know how many images would be possible on a hypothetical TV screen.
From Ask Dr. Math, a Forum special outreach project (high school collection)
- Seating People in a Row (Lasalle) 12/16/95
Find the numbers of ways in which 4 boys and 4 girls can be seated in a row of 8 seats if they sit alternately...
From Ask Dr. Math, a Forum special outreach project (high school collection)
- Total of Possible Telephone Numbers (Rkbj) 1/23/96
Try to determine the total possible telephone numbers in the U.S. using the following: Area codes are three digits in which the middle digit is either 0 or 1 and the first digit can be anything but 0 or 1. No three exchange digits can be the same as the preceding area code.
From Ask Dr. Math, a Forum special outreach project (high school collection)
- Maximum Possible Combinations (Rues) 1/23/96
Which is the maximum number of possibilities that I can obtain for n=digit?
From Ask Dr. Math, a Forum special outreach project (high school collection)
- Combinations of Letters and Numbers (Hansen) 3/19/96
A moped license plate has two letters and then four numbers in it. How many plates can be made without duplicating?
From Ask Dr. Math, a Forum special outreach project (high school collection)
- Possible Combinations on a Push Lock (Shirt) 4/17/96
A combination lock consist of a sequence of 'pushes' and each push is a collection of buttons (1 or more) that are pushed together.
From Ask Dr. Math, a Forum special outreach project (high school collection)
- Lottery Permutations (Dellinger) 5/16/96
Determine the number of unique permutations of a lottery where you pick 6 numbers out of 49, and numbers may not repeat...
From Ask Dr. Math, a Forum special outreach project (high school collection)
- Combinatorics: Unique Groupings (Corin) 5/30/96
Twenty-four friends want to play as many rounds of golf as they can... how many unique rounds of golf can they play?
From Ask Dr. Math, a Forum special outreach project (high school collection)
- Combinations and (Bond) 6/11/96
There are 6 boys and four girls. The boys do not have to stand together but they must be in order from shortest to tallest. Of these ten people, how many ways can they line up together?
From Ask Dr. Math, a Forum special outreach project (high school collection)
- Permutations and Combinations (Jain) 10/22/96
How many different six-digit numbers can be formed using three 5's, two 4's, and one 6?
From Ask Dr. Math, a Forum special outreach project (high school collection)
- Shaking Hands - How many were at the party? (Cheng) 6/20/96
Each person shook hands with everyone else. Mr. Li shook hands with 3 times as many men as women. Mrs. Li shook hands with 4 times as many men as women.
From Ask Dr. Math, a Forum special outreach project (high school collection)
- Connect 4 - Number of Winning Arrangements (HFSchool) 6/20/96
Can you help us find the formula for the number of winning lines on a 7 x 6 Connect-4 board?
From Ask Dr. Math, a Forum special outreach project (high school collection)
- Handshakes at a Party (Stuart) 6/23/96
At a party, everybody shakes hands with each other once. There are 45 handshakes. How many people are there at the party?
From Ask Dr. Math, a Forum special outreach project (high school collection)
- Re-seating a Thousand People (Gellman) 6/30/96
Can a thousand people seated around a circle in seats from 1 to 1000 be re-seated so as to preserve their order but with no person's number same as that of his chair?
From Ask Dr. Math, a Forum special outreach project (high school collection)
- Social Insurance Number (Steven) 7/3/96
Make a valid Social Insurance Number that has 8 as its check digit.
From Ask Dr. Math, a Forum special outreach project (high school collection)
- Number of Possible Telephone Numbers (Yulam) 7/15/96
How many phone numbers are there given the following restrictions on
certain digits of the number....?
From Ask Dr. Math, a Forum special outreach project (high school collection)
- Combinatorial Proof (Turner) 7/16/96
How do I prove that C(n,r)C(r,k) = C(n,k)C(n-k,r-k) where k <= r <= n?
From Ask Dr. Math, a Forum special outreach project (high school collection)
- Multiplying Groups of Numbers (Sasson) 5/9/96
Arrange the nine digits 1-9 into three groups...
From Ask Dr. Math, a Forum special outreach project (high school collection)
- Partitions of Set {1,2,3, ...n} (Scott) 7/25/96
Is there a generic way or some formula to count the partitions of the
set {1,2,3, ...n}?
From Ask Dr. Math, a Forum special outreach project (high school collection)
- Binomial Expansions and Pascal's Triangle (Fama) 7/10/96
What are binomial expansions and where can they be used?
From Ask Dr. Math, a Forum special outreach project (middle school collection)
- Probability Question from a Math Test (Matt) 3/8/96
There are 15 homerooms in the school and 20 students in each homeroom. If the principal selects 5 of the homerooms for a pizza party, what is the probability of Mr. Smith's homeroom being selected?
From Ask Dr. Math, a Forum special outreach project (middle school collection)
- Generating Possible Lottery Outcomes (Cain) 3/29/96
What math rule would I need to follow if I wanted to generate all possible combinations in a 50 number draw 6 lottery?
From Ask Dr. Math, a Forum special outreach project (middle school collection)
- Possible Combinations (Cox) 4/17/96
My teacher found a master lock. On the lock there were 4 sections which held 10 numbers, 0 - 9. He asked us to tell him how many different combinations were possible.
From Ask Dr. Math, a Forum special outreach project (high school collection)
- Craps (Mike) 5/24/96
Can you give me information on the probability and outcome of the game craps?
From Ask Dr. Math, a Forum special outreach project (high school collection)
- Slot Machines (Robbins) 5/29/96
What are the probabilities and mathematical expectations of slot machines?
From Ask Dr. Math, a Forum special outreach project (high school collection)
- Probability of Two Male Children (McClory) 7/5/96
If a family has two children, and the older child is a boy, there is a 50 percent chance the family will have two boys. However...
From Ask Dr. Math, a Forum special outreach project (high school collection)
- Probability of Drawing an Ace (Nstn) 5/31/96
If I had 40 cards and there were 4 aces in the deck...
From Ask Dr. Math, a Forum special outreach project (high school collection)
- An Explanation of Pascal's Triangle (Dortman) 2/27/95
My 10th grade daughter is having trouble finding a simple explanation of Pascal's Triangle and its application.
From Ask Dr. Math, a Forum special outreach project (high school collection)
- Tying Up Loose Ends to Create Different Size Loops (Taylor) 10/3/95
Wandelina has six identical pieces of string held firmly in her fist, with one end of each sticking out above her fist, and the other end of each sticking out below her fist. Different people come along and tie the ends above her hand together, and tie the ends below her hand together. When Wandelina opens her fist and looks at the strings, what combinations of different size loops might there be? What is the probability of each possible combination occurring?
From Ask Dr. Math, a Forum special outreach project (high school collection)
- Probability of Winning a Solitaire Game (Tsjrg) 10/26/95
I am interested in finding out how to figure the probability of winning the solitaire 'clock game'.
From Ask Dr. Math, a Forum special outreach project (high school collection)
- Probability of Picking in the Correct Order (Damour) 4/12/96
Out of a population of 200 different amino acids, what is the probability of selecting the correct 20 acids in the correct order on your first try.
From Ask Dr. Math, a Forum special outreach project (high school collection)
- Probability: Five and Seven Card Stud (Staas) 6/7/96
We are trying to figure out how to calculate the probability of getting two pair and three of a kind in five and seven card stud.
From Ask Dr. Math, a Forum special outreach project (high school collection)
- Card Game Probability Question (Fred) 5/22/96
What is the probability of getting a spade, queen and diamond
From Ask Dr. Math, a Forum special outreach project (high school collection)
- Dice: Full House (Eastman) 6/28/96
What is the probability of rolling a full house with 5 six-sided dice?
From Ask Dr. Math, a Forum special outreach project (elementary school collection)
- Chessboard Squares (Moore) 11/7/94
We are students from Sherwood Elementary is Edmonds WA. We have been working on problems in which we investigate patterns and functions. We worked on a problem called the chessboard squares. We discovered that there are 204 squares on the board and we found several ways to look at it. We found that you would add the different squares - 1 + 4 + 9 + 16 + 25 + 36 + 49 + 64. We did this and it worked because of the pattern, but our teacher wants to know why it works and if there is a quick way to get to the answer. What if there was a 100 by 100 board? Is there a way to use a function to find this out?
From Ask Dr. Math, a Forum special outreach project (middle school collection)
- Weighing Bales of Hay (Unknown) 2/2/96
You have 5 bales of hay. Instead of being weighed individually, they were weighed in all possible combinations of two...