SATHEE: Permutations And Combinations Question 151

Permutations And Combinations Question 151

Question: The number of ways in which four letters of the word ‘MATHEMATICS’ can be arranged is given by [Kurukshetra CEE 1996; Pb. CET 1995]

Options:

A) 136

B) 192

C) 1680

D) 2454

Show Answer

Answer:

Correct Answer: D

Solution:

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.

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Permutations And Combinations Question 151

Question: The number of ways in which four letters of the word ‘MATHEMATICS’ can be arranged is given by [Kurukshetra CEE 1996; Pb. CET 1995]

Options:

Answer:

Solution:

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