Permutations & Combinations
Grade 11
Question:
<p>How many different words can be made from the word <strong>ORDINATE</strong> so that the vowels occupy the odd places?</p>
<p style="display:inline">576</p>
<p style="display:inline">1680</p>
<p style="display:inline">96</p>
<p style="display:inline">420</p>
Step-by-Step Solution
Key Concept: Identify the specific odd-numbered positions for the vowels and apply the multiplication principle to combine the permutations of both vowels and consonants in their respective spots.
<p>There are 4 vowels and 4 consonants in the given word<br />
Number of ways to arrange 4 vowels at odd places = <sup>4</sup>P<sub>4</sub><br />
Also, number of ways to arrange 4 consonants at the even places = <sup>4</sup>P<sub>4</sub><br />
<span class="math-tex">\(\Rightarrow\)</span> The required number of words = <sup>4</sup>P<sub>4</sub> <span class="math-tex">\(\times\)</span> <sup>4</sup>P<sub>4</sub><br />
= 576</p>
Correct Answer: A