PERMUTATIONS AND COMBINATIONS

Front

What is a permutation?

Back

A permutation is an arrangement of objects in a specific order. The number of permutations of n distinct objects is n! (n factorial).

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 the formula C(n, r) = n! / (r!(n-r)!).

Front

How many different 5-digit numbers can be formed using the digits 1, 2, 3, 5, 7, and 8, if each digit may be used only once?

Back

720 different 5-digit numbers can be formed.

Front

How many of these 5-digit numbers are even and greater than 30000?

Back

168 5-digit numbers are even and greater than 30000.

Front

How many ways can two teams of 4 students be selected from a class of 8 boys and 6 girls, with one team containing boys only and the other girls only?

Back

1050 different ways to select the teams.

Front

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

Back

The formula is P(n, r) = n! / (n-r)!.

Front

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

Back

The formula is C(n, r) = n! / (r!(n-r)!).

Front

How many different teams of 6 tennis players can be chosen from 10 players (7 men and 3 women) if at least 1 woman must be included?

Back

203 different teams can be chosen.

Front

How many different committees of 8 people can be selected from 7 men and 5 women if the oldest man or the oldest woman, but not both, must be included?

Back

240 different committees can be selected.

Front

How many different 4-digit numbers can be formed from the digits 1, 2, 5, 7, 8, and 9 that are divisible by 5 and greater than 7000?

Back

36 different 4-digit numbers can be formed.