Permutation, Combination, and Counting Principal

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 given by n! / (n - r)!.

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 given by n! / (r! * (n - r)!).

Front

What is the counting principle?

Back

The counting principle states that if one event can occur in m ways and a second event can occur independently in n ways, then the two events can occur in m * n ways.

Front

How many ways can a student answer a multiple choice test with 15 questions and 5 options each?

Back

30,517,578,125 ways.

Front

How many ways can a disc jockey choose and arrange 3 songs from 9 available songs?

Back

504 ways.

Front

How many 5-digit passwords can be created if the first digit cannot be 0?

Back

90,000 possible passwords.

Front

How many ways can a president, vice-president, treasurer, historian, and secretary be selected from 24 members?

Back

5,100,480 ways.

Front

How many outfits can be made with 5 pairs of jeans, 8 t-shirts, and 2 pairs of shoes?

Back

80 outfits.

Front

What is the formula for permutations of n objects taken r at a time?

Back

nPr = n! / (n - r)!.

Front

What is the formula for combinations of n objects taken r at a time?

Back

nCr = n! / (r! * (n - r)!).