A) \[2454\]
B) \[2452\]
C) \[2450\]
D) \[1806\]
Correct Answer: A
Solution :
In a word EXAMINATION has \[2A,\,2I,\,2N,\,E,\,M,\,O,\,T,\,X,\] therfore 7 liters can be chosen in following ways Case I when 2 alike of one kind and 2 alike of second kind of is \[^{3}{{C}_{2}}\]. \[\therefore \] Number of words \[{{=}^{3}}{{C}_{2}}\times \frac{4!}{2!\,\,2!}=18\] Case II when 2 alike of one kind and 2 different ie, \[^{3}{{C}_{1}}{{\times }^{7}}{{C}_{2}}.\] \[\therefore \] Number of words \[{{=}^{3}}{{C}_{1}}{{\times }^{7}}{{C}_{2}}\times \frac{4!}{2!}\] \[=756\] Case III when all are different. ie, \[^{8}{{C}_{4}}\]. \[\therefore \] Number of words \[{{=}^{8}}{{C}_{4}}\times 4!=1680\] Hence, total number of words \[=18+756+1680\] \[=2454\]
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