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. ⁶⁴C₅

B. ⁶³C₄

C. ⁶⁵C₄

D. ⁶³C₅

Answer: Option B

Solution(By Examveda Team)

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 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 ⁶³C₄ ways.