Find the number of 6-digit numbers using the digits 3, 4, 5, 6, 7, 8 w

1.	Find the number of 6-digit numbers using the digits 3, 4, 5, 6, 7, 8 without repetition. How many of these numbers are(a) divisible by 5(b) not divisible by 5
Answer» 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 = 6! = 720 ways. (a) If the number is to be divisible by 5, the unit’s place digit can be 5 only. ∴ it can be arranged in 1 way only. The other 5 digits can be arranged among themselves in ⁵P₅ = 5! = 120 ways. ∴ Required number of numbers divisible by 5 = 1 × 120 = 120 (b) If the number is not divisible by 5, unit’s place can be any digit from 3, 4, 6, 7, 8. ∴ it can be arranged in 5 ways. Other 5 digits can be arranged in ⁵P₅ = 5! = 120 ways. ∴ Required number of numbers not divisible by 5 = 5 × 120 = 600

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

Answer»

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 = 6! = 720 ways.

(a) If the number is to be divisible by 5, the unit’s place digit can be 5 only.

∴ it can be arranged in 1 way only.
The other 5 digits can be arranged among themselves in ⁵P₅ = 5! = 120 ways.

∴ Required number of numbers divisible by 5 = 1 × 120 = 120

(b) If the number is not divisible by 5, unit’s place can be any digit from 3, 4, 6, 7, 8. ∴ it can be arranged in 5 ways.

Other 5 digits can be arranged in ⁵P₅ = 5! = 120 ways.

∴ Required number of numbers not divisible by 5 = 5 × 120 = 600