A five digit number divisible by 3 is to be formed using the numerals 0, 1, 2, 3, 4 and 5, without repetition. The total number of ways in which this can be done is
A. 216
B. 240
C. 600
D. 3125
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A.216
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 is5×4×3×2×1=120
Hence in total we have 120 +96 = 216 ways.
Hope it helps
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 is5×4×3×2×1=120
Hence in total we have 120 +96 = 216 ways.
Hope it helps
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