Question

Find the number of 6-digit numbers using the digits 3, 4, 5, 6, 7, 8 without repetition. How many of these numbers are not divisible by 5?

Answer 1

A number of 6 different digits is to be formed from the digits 3, 4, 5, 6, 7, 8 which can be done in ⁶P₆
i.e., 6! = 720 ways
If the number is not divisible by 5, then
Unit’s place can be any digit from 3, 4, 6, 7, 8 which can be selected in 5 ways.
Other 5 digits can be arranged in ⁵P₅ i.e., 5! ways
∴ Total number of ways in which numbers not divisible by 5 can be formed = 5 × 5! = 5 × 120 = 600