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

Note by Aishwarya Dadhich 2 years, 3 months ago

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\(\text{2 vowels can be chosen in } \binom{5}{2} , \text{3 consonants can be chosen in } \binom{17}{3}\)

\(\text{Next we observe that order isn't important so the vowels arrange themselves in 2! ways, consonants in 3!}\)

\(\text{No of words = } \binom{5}{2}\binom{17}{3}2!.3! = 10.17.15.16.2 = 81600\)

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is the answer 6800? ?

no , but whats your approach in solving this question?

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TopNewest\(\text{2 vowels can be chosen in } \binom{5}{2} , \text{3 consonants can be chosen in } \binom{17}{3}\)

\(\text{Next we observe that order isn't important so the vowels arrange themselves in 2! ways, consonants in 3!}\)

\(\text{No of words = } \binom{5}{2}\binom{17}{3}2!.3! = 10.17.15.16.2 = 81600\)

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is the answer 6800? ?

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no , but whats your approach in solving this question?

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