# Moderate Permutation-Combination Solved QuestionAptitude Discussion

 Q. $a,b,c,d$ and $e$ are five natural numbers. Find the number of ordered sets $(a,b,c,d,e)$ possible such that $a+b+c+d+e =64$.
 ✖ A. ${^{64}C_5}$ ✔ B. ${^{63}C_4}$ ✖ C. ${^{65}C_4}$ ✖ D. ${^{63}C_5}$

Solution:
Option(B) is correct

Let assume that there are 64 identical balls which are to be arranged in 5 different compartments (Since $a,b,c,d,e$ are distinguishable) If the balls are arranged in a row. i.e.,

$o,o,o,o,o,o......(64\text{ balls})$

We have 63 gaps where we can place a wall in each gap, since we need 5 compartments we need to place only 4 walls.

We can do this in ${^{63}C_4}$ ways.

## (2) Comment(s)

Hari
()

how would it became 4 walls for 5compartments...as we need (a,b,c,d,e)--five letters..???

Shubham Kumar
()

So if you add 4 compartments then you will have 5 divisions which will lead to 5 numbers as asked in question