Permutations & Combinations
Grade None
Question:
<p>How many 4-letter words can be made from the word <strong>MATHEMATICS</strong> such that no letter is repeated?</p>
<p style="display:inline">990</p>
<p style="display:inline">330</p>
<p style="display:inline">1680</p>
<p style="display:inline">7920</p>
Step-by-Step Solution
Key Concept: Identify the number of distinct letters available and calculate the permutations by selecting and then arranging the required number of letters from that set.
<p>There are letters of different kinds in the given word, namely, M, A, T, H, E, I, C, S.<br />
Number of ways to choose 4 letters from 8 = <sup>8</sup>C<sub>4</sub> = 70<br />
These 4 letters can be arranged in <sup>4</sup>P = 24 ways<br />
<span class="math-tex">\(\Rightarrow\)</span> Required number of words = 70 <span class="math-tex">\(\times\)</span> 24 = 1680</p>
Correct Answer: C