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How many different words, each containing 2 vowels and 3 consonants, can be formed with 5 vowels and 17 consonants?

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Two vowels can be selected in 5C2 ways. 

Three consonants can be selected in 17C3 ways. 

∴ 2 vowels and 3 consonants can be selected in 5C2 × 17C3 ways. 

Now, each group of 2 vowels and 3 consonants can be arranged in 5 ! ways. 

∴ The total number of words = 5C2 × 17C3 × 5 ! = 816000.

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