Drexel dragonThe Math ForumDonate to the Math Forum

Ask Dr. Math

High School Archive

Dr. Math Home || Elementary || Middle School || High School || College || Dr. Math FAQ

This page:
  permutations/combinations checkmark

  Dr. Math

See also the
Dr. Math FAQ:
  permutations and

Internet Library:


About Math

   basic algebra
   linear algebra
   linear equations

Complex Numbers

Discrete Math

Fibonacci Sequence/
  Golden Ratio

     conic sections/
     coordinate plane
   practical geometry

Negative Numbers

Number Theory

Square/Cube Roots


Browse High School Permutations/Combinations

Stars indicate particularly interesting answers or good places to begin browsing.

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 Player B?

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 arranged?

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?

Page: [<prev]  1  2  3  4  5  6  7  8 [next>]

Search the Dr. Math Library:

Search: entire archive just High School Permutations and Combinations

Find items containing (put spaces between keywords):
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

[Privacy Policy] [Terms of Use]

Home || The Math Library || Quick Reference || Search || Help 

© 1994- The Math Forum at NCTM. All rights reserved.