**Correct option is A****Explanation :** since $17!$ Is divisible by 9 so sum of the digits $48+x+y$ must be divisible by 9 so, $x+y$ can be $15$ or $16$ Also $17!$ Is divisble by $11$ so $|10+x-y|$ must be multiple of $11$ or zero .The only possibility is $|x-y|=1$ So, $x+y=15$