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 divisible by 5?

Answer 1

We have to form 6 digit numbers using the digits 3, 4, 5, 6, 7, 8 without repetition.
Total number of ways of arranging 6 digits in six places = ⁶P₆ = 6!
= 6 × 5 × 4 × 3 × 2 × 1 = 720 ways
Here, the number is divisible by 5. So it will have the digit 5 in the unit’s place.
Hence, the unit’s place can be filled in 1 way.
The other five places can be filled in by the remaining 5 digits
(Since repetition is not allowed) in ⁵P₅ = 5! Ways.
Total number of ways in which numbers divisible by 5 can be formed = 1 × 5! = 120