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

The Correct Option is D

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