Statement-1: A 5-digit number divisible by 3 is to be formed using the digits 0,1,2,3,4,5 without repetition, then the total number of ways this can be done is 216. Statement-2: A number is divisible by 3, if sum of its digits is divisible by 3.

Options

A. Statement-1 is true, statement-2 is true, statement-2 is a correct explanation for statement-1
B. Statement-1 is true, statement-2 is true, statement-2 is not a correct explanation for statement-1
C. Statement-1 is true, statement-2 is false
D. Statement-1 is false, statement-2 is true

Answer

A

Explanation

We know that a number is divisible by 3, if the sum of its digits is divisible by 3. now, out of 0,1,2,3,4,5,6 if we take 1,2,4,5,6 or 1,2,3,4,5 or 0,3,4,5,6 or 0,2,3,4,6 or 0,1,3,5,6 or 0,1,2,4,5 or 0,1,2,3,6
`therefore`Total number of ways`=2xx.^(5)P_(5)+5xx(.^(5)P_(5)-.^(4)P_(4))`
`=240+480`
`=720`
Statement-1 is false, statement-2 is true.