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Browse High School Permutations/Combinations

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Choose Three People from Five [05/09/2001]
What do the fractions in the numerator and denominator mean? Where does the formula come from?

Choosing Computer Disks [12/01/2001]
A bin of computer disks contains a supply of disks from four different manufacturers. In how many ways can you choose 6 disks from the bin?

Combinations of Images on a TV Screen [12/6/1995]
I'd like to know how many images would be possible on a hypothetical TV screen.

Combinations of the Letters in a Name [03/04/1998]
A formula for the number of combinations of the letters in a name, however many times one letter appears in that name.

Combinatorics Basics [07/07/1997]
I need to prove that n chooses n-1 = n; e.g. C(n,n-1) = n.

Committee of Six [10/07/1999]
A club has 8 male and 8 female members and is choosing a committee of 6 members, 3 male and 3 female. How many different committees can be chosen?

Counting Answer Keys [05/25/2001]
A multiple-choice test has 30 questions, each with five choices. How many answer keys are possible?

From Rock-Paper-Scissors to Stars and Bars [06/17/2014]
An adult struggles to calculate multi-player Roshambo outcomes without explicitly enumerating clenched fists, open palms, and two fingers. Doctor Ian explains why neither permutations nor combinations applies to such a scenario of replacement without regard to order; Doctor Peterson introduces a new approach.

Handshakes and Polygon Diagonals [09/12/2001]
If a polygon has 42 sides, how many diagonals does it have?

Math Symbol for C [12/15/1997]
I am puzzled by one symbol of typing math. What does the upper case letter C mean? As in (2C1) (3C1) / (47C2) = 6/1081.

Number and Letter Combinations [07/29/1997]
How many possible combinations can a person make with the letters a-z and 1-9 starting from 1 digit and ending up with up to 8 digits?

Number of Combinations for 7 Dice [2/22/1995]
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?

Number of Possible Telephone Numbers [7/15/1996]
How many phone numbers are there given the following restrictions on certain digits of the number....?

Number of Squares in an NxN Square [7/29/1996]
How many squares are there in an 8 x 8 square? How many rectangles are there?

Odds vs. Probability [12/06/1996]
What's the probability that a man can draw the numbers 2 and 7 from a hat containing the numbers 1-8?

Pascal's Triangle and Binomial Coefficients [09/11/2001]
Why are Pascal's triangle and the binomial coefficients the same?

Pascal's Triangle and the Tower of Hanoi [08/07/1997]
There's a connection between Pascal's Triangle and the Tower of Hanoi game but I can't remember what it is!

Permutations and Combinations: Deriving Formulae [06/18/1998]
I have been trying to figure out how to arrive at the formula for calculating combinations.

Possible Letter Arrangements [07/05/2000]
Is there a formula I can use to quickly get the number of possible arrangements of five, six,or seven different letters?

Powerball Lottery: Odds of Winning a Prize [09/02/2001]
How are the Powerball lottery odds established?

Rank of the Word FOCUS [06/27/2003]
The letters 'CFOSU' are arranged in dictionary order. What is the rank of the word 'FOCUS' in this order?

Round Robin Tournament Schedule [03/31/2000]
Is there a systematic way to come up with a schedule for a round robin tournament for up to 32 teams, where each team plays every other team once?

Squares in Rectangle Formula [06/30/2003]
What is the equation for the number of squares in a rectangle (like the chessboard puzzle)?

Ways To List 1, 2, ... 10 Out of Order [02/25/1997]
How many ways are there to list the numbers one through ten so that no number appears in its own position (i.e. 1 is not first in the list, 2 is not second...)?

20 Golf Players [04/11/1997]
How do you set up four teams such that the variance in the average team handicap is no more than one or two?

Algorithm for Derangements [01/11/2003]
I have been looking for a recursive algorithm to find all possible derangements of a set n.

Analyzing Prime Factors [06/14/2007]
Is there a number that has only three prime divisors (3, 5, and 7) and that has a total of 18 divisors?

Arrangement [07/12/1999]
How can I reduce the number of arrangements of the word ARRANGEMENT by using the probability of an occurrence?

Arrangements of 0's, 1's, and 2's [03/14/2002]
How many arrangements of six 0's, five 1's, and four 2's are there in which i) the first 0 precedes the first 1? ii) the first 0 precedes the first 1, precedes the first 2?

Arrangements of Letters [09/14/1999]
In how many ways can the letters in UNUNSUAL be arranged? For those arrangements, how many have all 3 U's together?

Arranging Letters [11/08/1998]
In how many ways can the letters in MISSISSIPPI be arranged? Suppose the 2 P's must be separated?... and other such problems.

Arranging Marbles in Boxes [09/16/1998]
Six marbles are placed in one of three different boxes. What is the probability that each box contains two marbles?

Arranging Things on a Shelf [05/05/2006]
Lucy has four vases--blue, yellow, red, and purple. How many ways can she arrange her vases in a row on a shelf?

Balls in Boxes [05/05/1999]
You have 2*t + 1 balls to put into 3 boxes, but the sum of the balls in 2 of the boxes should be more then the balls in the other box...

Baseball Batting Orders [10/14/2001]
How many possible batting orders are there for a team of nine players?

Beads on a Bracelet [05/04/1997]
How many different arrangements of 3 red and 3 blue beads on a bracelet are there?

Bell Number [02/24/2002]
I am trying to figure out how many different groups 50 people can be partitioned into.

Bell Numbers [08/29/2001]
I am looking for the formula for the number of different groups we can split a group of n different items into - order does not matter.

Binomial Probability [04/14/1999]
A multiple-choice exam probability question.

Blocks of Seats [11/08/1998]
In a row of 20 seats, in how many ways can 3 blocks of consecutive seats with 5 seats in each block be selected? And more such problems...

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