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  4. The remainder obtained when 1! + 2! + ... + 95! is divided by 15 is

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Q. The remainder obtained when $1! + 2! + ... + 95!$ is divided by $15$ is

WBJEEWBJEE 2012Permutations and Combinations

Solution:

Since, $1 !=1,2 !=2,3 !=6,4 !=24,5 !=120$
Since, all terms from $5 !$ onwards are divisible by 15 and $1 !+2 !+3 !+4 !=33$
$\therefore $ The required remainder after dividing by 15 will be 3.