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UGC-NET | UGC NET CS 2015 Jun – II | Question 3

  • Last Updated : 10 May, 2018

In how many ways can 15 indistinguishable fish be placed into 5 different ponds, so that each pond contains atleast one fish ?
(A) 1001
(B) 3876
(C) 775
(D) 200


Answer: (A)

Explanation: According to given question we have 15(n) fish and 5(r) pond:
We have to place fish in each pond so that there will be atleast one fish in each pond.
i.e. x1 + x2 + x3 + x4 + x5 = 15
n – 1Cr – 1
= 15 – 1C5 – 1
= 14C4
= 14! / (10!* 4!)
= 14 * 13 * 12 * 11 * 10! / (10! * 4!)
= 14 * 13 * 12 * 11 / 4!
= 1001
So, option (A) is correct.


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