Question:
The number of ways in which four letters of the word MATHEMATICS can be arranged is
The number of ways in which four letters of the word MATHEMATICS can be arranged is
Updated On: Oct 10, 2024
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- 2454
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The Correct Option is D
Solution and Explanation
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
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
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