Combinations and Arrangements Problems

Front

What is a combination?

Back

A combination is a selection of items from a larger set where the order does not matter.

Front

What is a permutation?

Back

A permutation is an arrangement of items where the order does matter.

Front

How do you calculate the number of combinations of n items taken r at a time?

Back

The formula is C(n, r) = n! / (r!(n - r)!), where n is the total number of items and r is the number of items to choose.

Front

How do you calculate the number of permutations of n items?

Back

The formula is P(n) = n!, where n is the total number of items.

Front

What is the difference between combinations and permutations?

Back

Combinations do not consider order, while permutations do.

Front

How many ways can you arrange the letters in the word 'APPLE'?

Back

60 ways.

Front

If you have 14 candy bars, how many ways can you choose 5?

Back

2002 ways.

Front

What is the formula for calculating distinguishable permutations of a multiset?

Back

The formula is n! / (n1! * n2! * ... * nk!), where n is the total number of items and n1, n2, ..., nk are the counts of each distinct item.

Front

How many ways can you choose 3 different kinds of cookies from 12 kinds?

Back

220 ways.

Front

What is the factorial of a number?

Back

The factorial of a number n (denoted as n!) is the product of all positive integers up to n.