Question

# The number of ways in which four letters of the word MATHEMATICS can be arranged is given by:

A
136
B
192
C
1680
D
2454

Solution

## The correct option is B $$2454$$Two pairs of identical letters can be arranged in $$^3C_2\dfrac {4!}{2!2!}$$ ways. Two identical letters and two different letter can be arranged in $$^3C_1\times {}^7C_2\times \dfrac {4!}{2!}$$ ways. All different letters can be arranged in $${}^8P_4$$ ways.$$\therefore$$ Total number of arrangements$$={}^3C_2\dfrac {4!}{2!2!}+{}^3C_1\times {}^7C_2\times \dfrac {4!}{2!}+\dfrac {8!}{4!}=2454$$.Maths

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