How many four-digit numbers Will not exceed 7432 if they are formed using the digits 2, 3, 4, 7 without repetition?

#### Solution

Among many sets of digits, the greatest number is possible when digits are arranged in descending order.

∴ 7432 is the greatest number, formed from the digits 2, 3, 4, 7.

∴ Since a 4-digit number is to be formed from the digits 2, 3, 4, 7, where repetition of digit is not allowed.

∴ 1000’s place digit can be selected in 4 ways.

100’s place digit can be selected in 3 ways.

10’s place digit can be selected in 2 ways.

Unit’s place digit can be selected in 1 way.

∴ Total number of numbers not exceeding 7432 that can be formed from the digits 2, 3, 4, 7

= Total number of four-digit numbers formed from the digits 2, 3, 4, 7

= 4 × 3 × 2 × 1 = 24