A) 136
B) 192
C) 1680
D) 2454
Correct Answer: D
Solution :
[d]: Word 'MATHEMATICS' has 2M, 2T, 2A, H, E, I, C, S. Therefore 4 letters can be chosen in the following ways. Case I: 2 alike of one kind and 2 alike of second kind i.e.,\[^{3}{{C}_{2}}\Rightarrow \]No. of words \[{{=}^{3}}{{C}_{2}}\frac{4!}{2!2!}=18\] Case II: 2 alike of one kind and 2 different i.e.,\[^{3}{{C}_{1}}{{\times }^{7}}{{C}_{2}}\] \[\Rightarrow \]No. of words \[{{=}^{3}}{{C}_{1}}{{\times }^{7}}{{C}_{2}}\times \frac{4!}{2!}=756\] Case III: All are different i.e., \[^{8}{{C}_{4}}\] \[\Rightarrow \]No. of words \[{{=}^{8}}{{C}_{4}}\times 4!=1680\]. Hence total number of words are 2454.
You need to login to perform this action.
You will be redirected in
3 sec
