How many words, each of 3 vowels and 2 consonants

Question:

How many words, each of 3 vowels and 2 consonants, can be formed from the letters of the word ‘INVOLUTE’?

 

Solution:

In the word ‘INVOLUTE’ there are 4 vowels, ‘I’,’O’,’U’ and ‘E’ and there are 4

consonants, 'N','V','L' and 'T'. 3 vowels out of 4 vowels can be chosen in ${ }^{4} \mathrm{C}_{3}$ ways. 2 consonants out of 4 consonants can be chosen in ${ }^{4} \mathrm{C}_{2}$ ways. Length of the formed words will be $(3+2)=5 .$ So, the 5 letters can be written in $5 !$ Ways. Therefore, the total number of words can be formed is $=\left({ }^{4} \mathrm{C}_{3} \times{ }^{4} \mathrm{C}_{2} \times 5 !\right)=2880$.

 

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