13.2 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

How many 2-digit numbers can be formed using the digits 1, 2, 3, and 4 without repeating digits?

Back

12 (4 choices for the first digit and 3 choices for the second digit: 4 x 3 = 12).

Front

How many ways can you arrange 4 songs from a selection of 12?

Back

11,880 (Using the formula P(12, 4) = 12! / (12 - 4)! = 12! / 8! = 12 x 11 x 10 x 9 = 11,880).

Front

How many ways can a club select a president, vice president, and secretary from 5 people?

Back

60 (Using the formula P(5, 3) = 5! / (5 - 3)! = 5! / 2! = 5 x 4 x 3 = 60).

Front

How many ways can a coach arrange a batting order for 10 players?

Back

3,628,800 (Using the formula P(10, 10) = 10! = 3,628,800).

Front

How many identification codes can be formed using 4 letters with no repetition?

Back

358,800 (Using the formula P(26, 4) = 26! / (26 - 4)! = 26 x 25 x 24 x 23 = 358,800).

Front

What is the difference between permutations and combinations?

Back

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

Front

What is the significance of the '!' symbol in permutations?

Back

'!' denotes factorial, which is the product of all positive integers up to that number.