First slide

Permutations

Question

A five digit number divisible by 6 is to be formed by using the digits 0, 1, 2, 3, 4 and 8 without repetition. The total number of ways in which this can be done is

Moderate

A

216
B

150
C

116
D

98

Solution

Since $0 + 1 + 2 + 3 + 4 + 8 = 18,$ the $5$ digit number will be divisible by 3 if either 0 or 3 is not used. When 0 is not used. For the unit place we have 3 choices $(2, 4 o r 8)$ and for the remaining place we have $4!$ Choices.
When 3 is not used In this case, 0 is used at the unit’s place, the number of choices is $4!$ If 0 is not used at the unit’s place, then unit’s place can be filled up in 3 ways and the remaining places in $(4! - 3!)$ ways. Thus, required number of numbers
$= 3 (4!) + 4! + 3 (4! - 3!) = 150$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App