Question 108

Out of 8 consonants and 5 vowels, how many words can be made, each containing 4 consonants and 3 vowels?

Solution

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Out of 8 consonants and 5 vowels selecting 4 consonants and 3 vowels can be done in $$^8C_4 * ^5C_3 = \dfrac{8*7*6*5*5*4}{4*3*2*2}$$
= 700
Internal arrangement of 7 letters = 7!
Thus, the total number of ways = 7!*700 = 352800
Hence, option C is the correct answer.

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