# 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}

**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 rowi.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

^{63}C

_{4}ways.

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what if a restriction is given that a>5,b>6 and c>7 then what extra needs to be substracted?