Question

a five-digit number divisible by 4 is to be formed using numerical 0 1 2 3 4 5 6 and 7 without repetition. the total number of ways

Answer 1

A number is divisible by 3 if the sum of the digits of the number is divisible by 3 . So from 1 ,2 , 3 , 4,5 we get -
0,1,2,4,5 and 1,2,3,4,5 
Where the sum of the 5 digits is divisible by 3.
Now let's take 0,1,2,4,5 first .

For the first place we have 4 numbers (0 excluded) ,for the second place we have 4 (now 0 included) ,for third 3 ,for fourth 2 and for fifth 1. Hence the number of choices we have is 4×4×3×2×1=96 .

Now we take 1,2,3,4,5
 Here the number of choices we have is 5×4×3×2×1=120

Hence in total we have 120 +96 = 216 choices
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