9.6 Permutations

Front

What is a permutation?

Back

A permutation is an arrangement of objects in a specific order. The order of arrangement is important.

Front

How do you calculate the number of permutations of n objects taken r at a time?

Back

The formula is P(n, r) = n! / (n - r)!, where n is the total number of objects and r is the number of objects to arrange.

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 from 1 to n.

Front

Calculate 5! (5 factorial).

Back

5! = 5 × 4 × 3 × 2 × 1 = 120.

Front

If there are 6 different organizations, how many ways can you award 1st, 2nd, and 3rd prizes?

Back

Using permutations, P(6, 3) = 6! / (6 - 3)! = 6 × 5 × 4 = 120.

Front

How many ways can you choose a president and vice-president from 24 members?

Back

Using permutations, P(24, 2) = 24! / (24 - 2)! = 24 × 23 = 552.

Front

What is the difference between permutations and combinations?

Back

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

Front

How many ways can you choose a manager and assistant from a 9-person task force?

Back

Using permutations, P(9, 2) = 9! / (9 - 2)! = 9 × 8 = 72.

Front

Is the order of arrangement important in combinations?

Back

No, the order of arrangement is not important in combinations.

Front

How many ways can you form a team of 3 players from 10 individuals?

Back

Using combinations, C(10, 3) = 10! / (3!(10 - 3)!) = 120.