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- Bridge Hand Probability [12/02/2008]
While playing Bridge, your hand has 9 cards in two suits (5 in one and
4 in the other). What is the probability of your partner having 4
cards in one of your two suits?
- Buying Doughnuts [03/22/2002]
Janine wants to buy three doughnuts, and there are five varieties to
choose from. She wants each doughnut to be a different variety. How many
combinations are there?
- Calculating Number of Possible Subsets of a Set [06/14/2002]
What is the formula for calculating the number of posssible subsets
for a finite set?
- Calculating Permutations [05/29/2001]
Please explain the formula for calculating the total possible number of
ways to choose r objects out of a total n objects.
- Catalan Numbers and Probability [05/29/2003]
Twenty persons want to buy a $10 ticket each. Ten of them have a $10
note and others have a $20 note. The person at the ticket counter has
no money to start with. What is the probability that the person at the
ticket counter will not have a change problem?
- Cent mille milliards de poemes [02/12/2000]
Question submitted via WWW: Hello. I have this problem and I've been
doing research to find the answer but I've had no luck. How did Queneau
fit 10^14 poems into ten pages?
- Change for a Dollar [03/07/1999]
How many different ways are there to make a change for a dollar?
- Checkerboard Chase [12/13/2002]
Player A begins by placing a checker in the lower left-hand corner
of a checkerboard (8 by 8 squares). Player B places a checker one
square to the right or one square up or one square diagonally up and
to the right of Player A's checker... Would you rather be Player A or
- Checkerboard Combinations [03/21/2001]
What is the possible number of combinations on a checkerboard with 12 (or
fewer) red pieces and 12 (or fewer) black pieces?
- Checkerboard Rectangles [03/24/2003]
A checkerboard has 8 horizontal boxes and 8 vertical boxes. How many
rectangles are possible inside that board?
- Checkerboard Squares [09/29/1997]
Suppose you have a square checkerboard not 8x8 - what is the easiest way
to find how many squares there are in it?
- Checkout Registers and Customers [02/27/2001]
Given two checkout registers and twenty customers, find a formula to
calculate how many different ways they can be arranged (order matters).
- Chess King Positions [03/06/2003]
Calculate the possible positions of two chess kings.
- The Chocolate Box Problem [11/11/2002]
Given twelve types of chocolates, what is the probability that a box
of fifty (randomly selected from an infinite supply with equal
probability), does not contain one or more of the types?
- Choose 11 Football Players in 12,367 Ways [9/16/1996]
A gym coach must select 11 seniors to play on a football team. If he can
make his selection in 12,376 ways, how many seniors are eligible to play?
- Choosing 3 of 6 Colors [03/03/2000]
Patrick has a box of crayons with red, blue, yellow, orange, green and
purple. How many different ways can Patrick select 3 colors?
- Choosing a Duet, Lead Singer/Backup [02/25/2002]
Twenty singers are trying out for a musical. In how many different ways
can the director choose a duet? In how many ways can the director choose
a lead singer and a backup?
- Choosing Socks [05/20/1999]
What are the steps to evaluate C(n,1); C(n,2) ?
- Choosing Three Numbers from 1-10 [06/08/2001]
How many ways can three numbers be chosen from the numbers
1,2,3,4,5,6,7,8,9,10 so that no two of the three numbers are consecutive?
- A Circular Massacre [09/25/1998]
Ten thousand sailors are arranged in a circle; starting with the first
one, every other sailor is pushed overboard ....
- Circular Permutations [08/07/2005]
With four card players at a round table, how many different seating
arrangements exist from a sequential point of view?
- C(n,0) = 1 [04/22/2003]
How is C(n,0) equal to 1, where n is an integer?
- C(n,r) Seeing Negative? [06/11/2010]
A student notices that calculators compute nCr for r > n, and wonders
about the combination function's "true" form. Doctor Vogler explains how
to extend various formulas to different types of arguments, including
non-integer and complex numbers.
- Co-efficient of an Algebraic Term [07/18/1999]
Simplify [z^40] (1 + z + z^2 + ... + z^9)^100.
- Coefficients in a Trinomial Expansion [04/24/2001]
In the expansion of (a+b+c)^6, what is the coefficient of a^2b^2c^2?
- Coin Patterns [08/26/2003]
Each of four rows of coins has exactly one penny, one nickel, one
dime, and one quarter. No row, either horizontal, vertical, or
diagonal, has more than one coin of each kind. How are the coins
- Coin Tosses, Dealing Cards... [12/08/1998]
Several questions on discrete math - probability and combination;
deducing recurrence relations.
- Collecting a Complete Set [03/15/2000]
I have a very large box filled with 8 different frying pan handles in
equal proportions. What is the probability that I will have to remove 32
handles before I get a complete set?
- Color Arrangements on the Face of a Cube [11/23/2001]
Given three colors in which to paint the face of a cube, red, blue, or
yellow. How many different color patterns are there if each face of the
cube must be painted red, blue, or yellow?
- Colors on the Rubix Cube [01/15/2005]
How many color combinations are there in a Rubix cube?
- Colour Combinations on a Cube [02/08/2002]
If each side of a cube is painted red or yellow or blue, how many
distinct colour patterns are possible?
- Combinations and Permutations [6/11/1996]
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?
- Combinations and Permutations with Replacement [02/01/2004]
I have found the formulas for permutations and combinations but both formulas appear to be for the cases where there is no replacement. Do you know the formulas for "with replacement"?
- Combinations for Casting a Play [11/15/1995]
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?
- Combinations of Combinations? [12/15/2003]
I understand the formula n!/((n-r)!*r!) to compute the number of
combinations of r objects selected from n objects. Now, having
determined nCr, how can I calculate the number of resulting
combinations which contain t items? Can I calculate that directly at
the start without first finding all the initial combinations?
- Combinations of Cubes [11/07/1996]
How many different cuboids can be made from one million connectable
cubes, using all the cubes?
- Combinations of Four-Digit PINs with Exactly Three Digits Different [08/06/2012]
A combinatorics student wonders why all four-digit PINs with exactly three different
digits does not amount to choosing three digits out of 10 without repetition. Doctor
Douglas explains how 10*9_C_2 differs from 10_C_3.
- Combinations of Letters [10/20/1998]
What is the general formula for counting the number of different ways to
combine the letters of one word? For example, Emma has 12 ways.
- Combinations of Letters and Numbers [3/19/1996]
A moped license plate has two letters and then four numbers in it. How
many plates can be made without duplicating?
- Combinations of Lottery Numbers [8/5/1995]
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 entries?