Permutations & Combinations

Front

What is a permutation?

Back

A permutation is an arrangement of objects in a specific order. The number of permutations of n objects taken r at a time is denoted as nPr.

Front

What is a combination?

Back

A combination is a selection of objects without regard to the order. The number of combinations of n objects taken r at a time is denoted as nCr.

Front

What is the formula for permutations?

Back

The formula for permutations is nPr = n! / (n - r)!, where n is the total number of items, and r is the number of items to arrange.

Front

What is the formula for combinations?

Back

The formula for combinations is nCr = n! / [r!(n - r)!], where n is the total number of items, and r is the number of items to choose.

Front

How many ways can 9 players be arranged in a batting order?

Back

nPr(9,9) = 362,880.

Front

How many ways can 3 flavors be selected from 15 ice cream flavors?

Back

nCr(15,3) = 455.

Front

How many ways can 4 crayons be selected from 16?

Back

nCr(16,4) = 1820.

Front

How many ways can a president, vice-president, and secretary be chosen from 20 members?

Back

nPr(20,3) = 6840.

Front

How many ways can a committee of 3 be selected from 8 members?

Back

nCr(8,3) = 56.

Front

What is the difference between permutations and combinations?

Back

Permutations consider the order of selection, while combinations do not.