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  4. The ten's digit in 1 ! + 4 ! + 7! + 10!+ 12! + 13! + 15! + 16! + 17! is divisible by

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Q. The ten's digit in $1 ! + 4 ! + 7! + 10!+ 12! + 13! + 15! + 16! + 17!$ is divisible by

COMEDKCOMEDK 2010Permutations and Combinations

Solution:

$1! = 1 \Rightarrow $ ten's digit = 0
$4! = 24 \Rightarrow $ ten's digit = 2
$7! = 5040 \Rightarrow $ ten's digit = 4
Now, $10!, 12!, 13!, 15!, 16!$ and $17!$ have ten's digit = 0
Hence, ten's digit of $1! + 4! + 7! + 10! + 12! + 13! + 15! + 16! + 17!$ is $0 + 2 + 4 + 0 = 6$ which is divisible by $3!$.