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Question
How many different words, each containing 2 vowels and 3 consonants can be formed with 5 vowels and 17 consonants?
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Solution
2 out of 5 vowels and 3 out of 17 consonants can be chosen in \[{}^5 C_2 \times {}^{17} C_3\] ways.
Thus, there are \[{}^5 C_2 \times {}^{17} C_3\]groups, each containing 2 vowels and 3 consonants.
Each group contains 5 letters, which can be arranged in
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