GATE | GATE-IT-2004 | Question 35

In how many ways can we distribute 5 distinct balls, B1,B2,…,B5 in 5 distinct cells, C1,C2,…,C5 such that Ball B,is not in cell C,Vi=1,2,…,5 and each cell contains exactly one ball?
(A) 44
(B) 96
(C) 120
(D) 3125

Answer: (A)

Explanation: Total permutations possible = 5!=120

Possible number of ways in which at least one ball is in cell = 5C1*4! – 5C2*3! + 5C3*2! – 5C4*1! + 1 = 76


So answer is A

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