$17!=3556xy428096000,$then $(x+y)$ equals?(without using a calculator) $17!=3556xy428096000,$then $(x+y)$ equals?
a)$15$ b)$6$ c)$12$ d)$13$
With help of calculator $(x+y)$ can be easily calculated as $15$.But without a calculator,I can only conclude that the sum of digits $(3+5+5+6+x+y+4+2+8+9+6)$ is a multiple of $3$, & excluding $(x+y)$ the sum of the digits $(3+5+5+6+4+2+8+9+6) =48$.Thus excluding option d) the ans can be any of a),b) or c).
Please help me to find the exact answer.
Thank you 

First use the fact that the factorial is divisible by $9$, and therefore the digit sum is divisible by $9$. 
Then use the fact that the number with decimal representation $abcdefg\dots$ is divisible by $11$ if and only if $a-b+c-d+e-f+\cdots$ is divisible by $11$.
