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ISI2020-MMA: 17

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The number of words that can be constructed using $10$ letters of the English alphabet such that all five vowels appear exactly once in the word is

  1. $^{21} \text{C}_{5} \;10!$

  2. $^{21} \text{C}_{5} \;(5!)^{2}$

  3. $^{10} \text{P}_{5} \; ^{21} \text{P}_{5} $

  4. $^{10} \text{P}_{5} \;(21)^{5}$

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The number of words that can be constructed using 10

 letters of the English alphabet such that all five vowels appear exactly once in the word.

 

The location of the vowel can be chosen in 10C5

 ways and that also can be filled in 5!

 ways, and the remaining 5

 locations can be filled by pow(21,5)

 ways.
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