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

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

∴ Required number of numbers not divisible by 5

= 5 × 5!

= 5 × 120

= 600