Question

If all the letters of the word MASTER are permuted in all possible ways and words (with or without meaning) thus formed are arranged in dictionary order, then the rank of the word MASTER is:

• A. 357
• B. 527
• C. 257
• D. 752

Hint:

For finding the rank of a word in a dictionary arrangement, use the factorial method by counting how many words can be formed with the available letters before the given word.

Answer 1

The Correct Option is C

The word "MASTER" has 6 letters, with the following frequencies: M, A, S, T, E, R (all distinct). The total number of permutations of the letters of the word is \( 6! = 720 \). Step 1: To find the rank of the word "MASTER," we count the number of words that come before it in dictionary order. 1. First, count all permutations that start with a letter less than M (i.e., A, E, R, S, T).
2. Then, fix M, and count permutations starting with MA, MS, etc., until we reach MASTER. After computing the number of words that come before "MASTER," the rank is found to be 257.