Permutations & Combinations
Grade None
Question:
<p>If the letters of the word MATHS are permuted and all possible words so formed are arranged as in a dictionary with serial numbers, then the serial number of the word THAMS is</p>
<p style="display:inline">102</p>
<p style="display:inline">104</p>
<p style="display:inline">103</p>
<p style="display:inline">101</p>
Step-by-Step Solution
Key Concept: The dictionary rank of a word is found by alphabetically ordering the letters and calculating the number of permutations for all words that appear lexicographically before the target word.
<p>A _ _ _ _ = 4!<br />
H _ _ _ _ = 4!<br />
M _ _ _ _ = 4!<br />
S _ _ _ _ = 4!<br />
T A _ _ _ = 3!<br />
T H A M S = 1<br />
Total = 4 <span class="math-tex">$\times$</span> 4! + 1 <span class="math-tex">$\times$</span> 3! + 1 = 103</p>
Correct Answer: C