Question

Seven different coins are to be divided amongst three persons. If no two of the persons receive the same number of coins but each receives atleast one coin & none is left over, then the number of ways in which the division may be made is k, then sum of the digits in number of k equals.

Answer 1

Well with Hence people and no. two people getting the same number (and everyone gets at least $1$) $-$ the only way is to divide it is $1-2-4$,

Assuming person one gets one coin... there are $7$ possibilities.

Person two gets $2$ coins from the remaining $6$

$=\frac{6!}{(6-2)!2!}=15$

(because order of the coin does not matter).

Person $3$ gets what's left $-$ $4$ wins ($1$ possibility again order does not matter)

but there are also $6$ ways to average the people.....

$7\times 15\times 6=630$