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

There are 6 different digits and we have to form 6-digit numbers, i.e., n = 6, r = 6

If no digit is repeated, the total numbers with 6-digits can be formed = ⁿP_r

= ⁶P₆

= 6!

= 6 x 5 x 4 x 3 x 2 x 1

= 720.

Since the number is divisible by 5, the unit's place of 6-digits number can be filled in only one way by the digit 5.

Remaining 5 positions can be filled from the remaining 5 digits in ⁵P₅  ways.

Hence, the total number of 6-digit numbers divisible by 5 = 1 x ⁵P₅ = 5!

= 5 x 4 x 3 x 2 x 1

= 120.