Permutation-Combination
Aptitude

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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.

${^{63}C_5}$

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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