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A word has 8 consonants and 3 vowels. How many distinct words can be formed if 4 consonants and 2 vowels are chosen?

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There are 8 consonants and 3 vowels. From 8 consonants, 4 can be selected in 8C4

= 70 ways.

From 3 vowels, 2 can be selected in 3C2

= 3 ways.

Now, to form a word, these 6 ietters (i.e., 4 consonants and 2 vowels) can be arranged in

6P6 = 6! ways.

∴ Total number of words that can be formed

= 70 × 3 × 6!

= 70 × 3 × 720

= 151200

∴ 151200 words of 4 consonants and 2 vowels can be formed.

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