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High School Archive

Browse High School Permutations/Combinations

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Painted Cube [06/21/2001]

I've done diagrams and tables, but can't find a formula for the problem.

Painted Cube Faces [03/22/2001]

Each face of a cube is to be painted either red or blue. How many different possible combinations are there, from all blue to all red faces and every combination in between?

Painting Cube Faces Green [08/19/2003]

How many cubes could be painted so that each cube is different from the other?

Palindromic Numbers [01/04/1998]

How many palindromic numbers exist that are less than 100,000?

Partitioning an Integer [11/14/1998]

How many different ways are there of making a number by adding different combinations of three numbers?

Partitioning Elements [12/08/2001]

If part(n,k) is the number of ways to partition a set of n elements into k subsets, what is Part(5,2)? Prove Part(n+1,k) = Part(n,k-1)+k* Part(n,k)...

Partitions of Set {1,2,3, ...n} [7/25/1996]

Is there a generic way or some formula to count the partitions of the set {1,2,3, ...n}?

Pascal's Triangle and Combinations [06/05/1998]

Can you show me why (n C r) + (n C r+1) = n+1 C r+1?

Pascal's Triangle: Words instead of Numbers [08/28/2001]

How many times can you read the word "triangles" in the figure?

Path Possibilities [10/24/1999]

How many combinations of moves are there to get from point A to point B in a modified checkerboard figure, assuming that you can only move right and up?

Paths on a Checkerboard [04/18/1999]

On an 8x8 checkerboard, how many paths are there from point A to point B following only the lines going downward and to the right?

Paths to Triangle Points [05/26/1999]

How can I find the number of paths to a point using Pascal's triangle?

Perfect Shuffle [09/09/2002]

If you were to shuffle a deck of cards perfectly, how many repetitions would it take to return to the original order?

Permutation and Combination Equality [07/18/1999]

Prove that (nC0)^2 + (nC1)^2 + (nC2)^2 + ... + (nCn)^2 = (2nCn), where nCi = n!/((n-i)!*i!).

Permutation, Combination, and Repetition [11/25/1998]

What is a permutation and what is a combination with repetition and no repetition?

Permutation Formula [4/23/1995]

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.

Permutation Groups Generated by 3-Cycles [05/14/2003]

Show A_n contains every 3-cycle if n >= 3; show A_n is generated by 3- cycles for n >= 3; let r and s be fixed elements of {1, 2,..., n} for n >= 3 and show that A_n is generated by the n 'special' 3-cycles of the form (r, s, i) for 1 <= i <= n.

Permutations [10/11/1997]

A number of X's and a number of Y's are written in a row such as XX.....XXYY.....Y - Investigate the number of different arrangements of the letters.

Permutations and Arithmetic Means [01/24/2003]

Demonstrate that in the (n!) permutation of the first n integers in a table of dimension n! rows and n columns, the arithmetic mean of the squares of each column terms is equal to (n+1)(4n+2)/12, and the arithmetic mean of the crossproduct between any two columns is equal to (n+1)(3n+2)/12.

Permutations and Combinations [10/22/1996]

How many different six-digit numbers can be formed using three 5's, two 4's, and one 6?

Permutations and Combinations [03/11/1998]

What is the difference between permutations and combinations?

Permutations, Combinations, Arrangements, and Strings [10/22/2007]

When a coin is tossed four times, is an outcome of HTTH considered a permutation, a combination, or something else entirely?

Permutations in a Necklace [07/04/1999]

What is the formula for the number of permutations in a necklace with the combination of AABB?

Permutations of 1234567890 [09/23/2001]

I'm trying to find a pattern in combinations and how many combinations there are in 1234567890.

Permutations of Beads on a Necklace [09/07/99]

What is the formula for the number of permutations in a necklace with the combination of AAABBB?

Permutations of Indistinguishable Objects [09/21/2000]

How many ways can eight dogwoods be planted?

Permutations of Vertices [04/22/1997]

If the vertices of a polygon are labeled with letters, in how many different ways can a quadrilateral or a pentagon be named?

Permutations or Combinations? [01/09/2003]

When given a permutation or combination problem, is there anything SPECIFIC to look for to know whether it is one or the other?

Phone Numbers With Duplicate Digits [03/25/2003]

Someone is trying to remember a phone number but cannot remember the whole thing. He remembers 279-XXXX and that the last 4 numbers must contain a 2 and a 7 and a 9. He only has 2, 7, or 9 as digits. How many possible completions are there?

Pieces on a Chess Board [10/27/1996]

Prove that with 9 separate playing pieces, you cannot place the pieces on an 8 by 8 chess board such that the distance between any 2 pieces is always different.

Placing Balls in Urns [05/15/2001]

Prove that the number of different ways we can place b indistinguishable balls in u distinguishable urns is C(b+u-1,b) = C(b+ u-1,u-1).

Poker Combinations [05/08/1997]

In a standard deck of cards, how many different ways are there to get a straight, a flush, a straight flush, one pair, or two pairs?

Poker, Probability, Combinatorics [11/04/1997]

If we deal n hands consisting of 2 cards each, what is the probability that there will be no pairs amoung the hands?

Polya's Counting Theory [09/12/2003]

In how many different ways could a 6-sided die be numbered?

Polynomial Expansion [02/06/2003]

What's the general formula for things like (a+b+c)^2; (a+b+c+d)^3; (a+ b+c+d+e)^4; (...n+1 terms...)^nth power?

Possible Combinations [4/17/1996]

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.

Possible Combinations from Cards Drawn at the Same Time? [04/02/1998]

If two of four numbered cards are drawn at the same time, how many possible combinations could be made?

Possible Combinations on a Push Lock [4/17/1996]

A combination lock consist of a sequence of "pushes" and each push is a collection of buttons (1 or more) that are pushed together.

Possible Combinations when Distributing Items Unevenly [05/24/2004]

There are 20 distinct toys to be handed out to 5 children. How many possible ways are there to hand them out if two children each get 7 toys and three children get 2 toys each?

Possible Paths across a Rectangular Grid [02/16/2005]

Consider a grid that has 3 rows of 4 squares in each row with the lower left corner named A and upper right corner named B. Suppose that starting at point A you can go one step up or one step to the right at each move. This is continued until the point B is reached. How many different paths from A to B are possible?

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