A) \[\frac{11!}{2!2!2!}\]
B) \[59\]
C) \[56\]
D) \[\frac{11!}{3!2!2!}\]
E) \[\frac{11!}{3!3!2!}\]
Correct Answer: B
Solution :
Word MEDITERRANEAN has\[2A,3E,ID,II,1M,\]\[2N,2R,IT\]. In out of four letter E and R is fixed and rest of the two letters can be chosen in following ways. Case I. Both letter are of same kind ie,\[^{3}{{C}_{2}}\] ways, therefore number of words \[{{=}^{3}}{{C}_{2}}\times \frac{2!}{2!}=3\] Case II. Both letters are of different kinds ie,\[^{8}{{C}_{2}}\]ways, therefore number of words \[{{=}^{8}}{{C}_{2}}\times 2!=56\] Hence, total number of words are\[56+3=59\]
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