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Browse High School Permutations/Combinations
Stars indicate particularly interesting answers or
good places to begin browsing.
 Number of Terms in a Polynomial Expansion [12/01/2005]

How would you calculate the total number of terms in the simplified
expansion of (a+b+c+d)^10? Is there a general formula for this?
 Occupancy Problem [08/06/2001]

Given n bins and m (indistinguishable) balls, how many arrangements are
possible such that no bin has greater than r balls?
 On Spins and Surprises [10/15/2011]

Nine consecutive spins of a roulette wheel surprise a gambler unfamiliar with how to
determine the likelihood of independent events. Doctor Vogler obliges with the
requested combinations and probabilities, but only after questioning our arbitrary
preference for some events over others that may have the same  or even longer 
odds.
 Onto Functions and Stirling Numbers [09/22/2002]

How would I show for m greater than or equal to 3 that s(m, m2) = (1/
24)m(m1)(m2)(3m1), where s(m,n) are Stirling numbers of the first
kind?
 Optimal Seating Arrangements [07/20/2000]

N people are invited to a party and asked to RSVP with the names of up to
k people they would like to sit with. Is there a formula that will yield
the "best" arrangement of people?
 Ordering Combinations, Then Picking the nth Item [10/22/2010]

How do you pick the nth combination without listing all the ones before it? Doctor
Vogler restores some order to an ambiguous objective, then outlines an algorithm for
sorting combinatorics.
 P(2n,3) = 2P(n,4) [10/08/2002]

Solve: P(2n,3) = 2P(n,4)
 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,k1)+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!/((ni)!*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 3Cycles [05/14/2003]

Show A_n contains every 3cycle 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' 3cycles 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 sixdigit 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 279XXXX 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+u1,b) = C(b+ u1,u1).
 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?
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