# Permutation and Combination problem : In how many ways can Rs. 16 be divided into 4 person when none of them get ...

4,033

## Solution 1

The easiest way to solve it is to imagine giving each person Rs. $3$ right away and then distributing the remaining Rs. $4$ arbitrarily. In other words, reduce the problem to distributing Rs. $4$ amongst $4$ people with no restrictions: you have the formula for that, with $n=r=4$:

$$\binom{4+4-1}{4-1}=\binom73=35\;.$$

## Solution 2

What you want is, how many ways are there to write $$\{1, \ldots, 16\} = A_1 \dot{\cup} A_2 \dot\cup A_3 \dot\cup A_4$$ Under the constraint, that $|A_i| \geq 3 \quad \forall\ i$.
Did I understand that correctly?

Share:
4,033

Author by

### Sachin

Updated on August 01, 2022

• Sachin 7 months

Permutation and Combination problem :

Problem : In how many ways can Rs. 16 be divided into 4 person when none of them get less than Rs. 3 ?

I have this : The number of ways of distributing $n$ things all alike into $r$ different groups is $^{n+r-1}C_{r-1}$ lots , no lots being blank:

Coefficient of $x^n$ in $(1+x+x^2+.....)^r$

I am unable to understand how to use this case in the given problem. Request you to please help me on this and elaborate a bit .. will greatful to you... Thanks...