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