# A 5-digit Number Divisible by 3 is to Be Formed Using the Digits 0, 1, 2, 3, 4 and 5 Without Repetition. the Total Number of Ways in Which this Can Be Done is , 216 , 600 , 240 , 3125 - Mathematics

MCQ

A 5-digit number divisible by 3 is to be formed using the digits 0, 1, 2, 3, 4 and 5 without repetition. The total number of ways in which this can be done is

• 216

• 600

• 240

• 3125

#### Solution

216
A number is divisible by 3 when the sum of the digits of the number is divisible by 3.
Out of the given 6 digits, there are only two groups consisting of 5 digits whose sum is divisible by 3.
1+2+3+4+5 = 15
0+1+2+4+5 = 12
Using the digits 1, 2, 3, 4 and 5, the 5 digit numbers that can be formed = 5!
Similarly, using the digits 0, 1, 2, 4 and 5, the number that can be formed = 5! - 4! {since the first digit cannot be 0}
∴ Total numbers that are possible = 5! + 5! - 4! = 240 -24 = 216

Concept: Permutations
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 16 Permutations
Q 15 | Page 47