Question

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

• A. 136
• B. 2454
• C. 1680
• D. 192

Answer 1

Answer: (D)

192

Answer 2

The correct option is (B); 2454
1st Case: 2 pair of identical letters can be arranged in ^3C_2$$\times$$\frac{4!}{2!2!}
2nd Case: 2 identical and different letters can be arranged in ^3C_1$$\times$$^7C_2$$\times$$\frac{4!}{2!}
3rd Case: All different letter can be arranged in $^8P_4$
$\therefore$ Total number of arrangements
^3C_2$$\times$$\frac{4!}{2!2!}+^3C_1$$\times$$^7C_2$$\times$$\frac{4!}{2!}+$^8P_4$=2454