A) 136
B) 126
C) 252
D) 525
E) None of these
Correct Answer: A
Solution :
Explanation Option (a) is correct. There are 11 letters in the given word of which 2 are A,s, 2 are I?s 2 are N?s and the remaining 5 letters are different. Thus we have 11 letters of 8 different kinds viz, (A, A), (I, I), (N, N) E, X, M, T, O. A group of 4 letters can be classified as follows: (i) Two alike of one kind and two alike of another kind. (ii) Two alike and the other two different. (iii) All four different. In case I, the number of ways = \[^{3}{{C}_{2}}=3\] Incase II, the number of ways = \[^{3}{{C}_{1}}{{\times }^{7}}{{C}_{2}}=63\] In case III, the number of ways = \[^{8}{{C}_{4}}=70\] Hence, the required number of ways \[=3+63+70=136\].
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