Question

In how many ways a 5 digit numbers divisible by 6 can be formed by the digits 0, 1, 2, 4, 5, 6 without repetition​

Answer 1

Answer:

108 is correct answer

I think it's help you

Answer 2

HELLO DEAR,

GIVEN:- A five digit number divisible by 6 is to be formed by using 0,1,2,3,4,5 without repetition.

To find the number of ways in which this can be done.

SOLUTION:-

We have to select such a way the arrangement of digits to make it divisible by 6.

And 6 is divisible by 2 and 3.

Therefore ,the number which is divisible by 6 is also divisible by 2 and 3.

we need to use the divisibility rules for both 2 and 3 .

The last digit is even is divisible by 2.

The sum of the digits is divisible by 3 then that number is divisible by 3.

First select the five digits whose sum is divisible by 3:

Sum of all givin digits = 15 which is a multiple of 3.

Case1:

1,2,3,4,5 are chosen.

For the number to be divisible by 2 last digit is 2 or 4.

Thus ,the number of ways = 4! ×2!

= 48.

Case2:-

0,1,2,4,5 are chosen.

a) if last two digit 0, number of ways = 4! = 24.

b) lyf last digit is to the other digits may be filled in from left to right

3×3×2×1= 18 ways

c) if last digit is 4 ,the other digits may be filled in from left to right,

3×3×2×1 = 18 ways

So, the answer = 48+24+18+18=108 ways.

I HOPE IT'S HELP YOU DEAR,

THANKS.