How many distinguishable permutations of the letters in the word BANANA are there ?
(A) 720
(B) 120
(C) 60
(D) 360
Answer: (C)
Explanation: In BANANA we have six letters in total but here we have some duplicate letters too so we have to deal with it and have to remove those duplicate case.
B – 1
A – 3
N – 2
So total no of words possible is factorial(6) ie 6! but we must remove duplicate words:
ie- (6!/(2!*3!))
which gives 60
So 60 distinguishable permutation of the letters in BANANA.
So, option (C) is correct.
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