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

1 year, 3 months ago

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

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

$$\text{No of words = } \binom{5}{2}\binom{17}{3}2!.3! = 10.17.15.16.2 = 81600$$ · 6 months, 3 weeks ago

is the answer 6800? ? · 1 year, 3 months ago