Question 41

The number of ways in which four letters of the word MATHEMATICS  can be arranged is

Solution

Letters of the word : 

M A T   H E I C S
M A T

Case 1 : 4 are different (all four words chosen are different, no repition)

= $$C^8_4\times4!=70\times24=1680$$

Case 2 : 2 alike + 2 different (out of the chosen four letters, two are same, rest two are chosen of the remaining seven)

= $$C^3_1\times C^7_2\times\frac{4!}{2!}$$

= $$3\times21\times12=756$$

Case 3 : 2 alike + 2 alike (four letters are chosen from M,A,T) 

= $$C^3_2\times\frac{4!}{2!2!}=18$$

$$\therefore$$ Total number of ways = $$1680+756+18=2454$$

=> Ans - (B)


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