41-52 Counting Permutations These exercises involve counting permutations.

Three-Digit Numbers How many different three-digit whole numbers can be formed by using the digits 1 , 3 , 5 , and 7 if no repetition of digits is allowed?

To find:

The number of different three-digit whole numbers formed by using the given digits.

Given:

The digits are 1, 3, 5, and 7 and the condition is that there is no repetition of digits.

Approach:

The number of permutations of n distinct objects taken r at a time is,

P(n,r)=n!(n−r)!

Calculation:

Total number of digits is 4 and repetition is not allowed.

Thus, the number of selecting different three-digit whole numbers from the 4 digits is given as,