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 at least one coin & none is left over, then the number of ways in which the division may be made is

• A. $420$
• B. $630$
• C. $710$
• D. none

Answer 1

The correct option is B $630$

We have $3$ peoples, $7$ coins and all must get at least 1 coin and every one get unequal coin.

Only way is $1-2-4$ coin.

Assuming 1st person gets one coin from there are $7$ ways for that.

Now person $2$ gets $2$ coin from remaining 6 so, no of ways$={}^6{C}_2$

$=15$

And person $3$ gets $4$ coins only $1$ way.

However its not necessary that only person 1 gets 1 coin, i.e. people needs to interchanged which is done in $3!$ ways.

So, total number of ways,

$=7\times 15\times 3!$

$=630.$

Hence, the answer is $630.$