Discussion

Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?

Answer: C

Choose the letters first, then arrange them.

\[ {}^{7}C_{3} \times {}^{4}C_{2} = 35 \times 6 = 210 \text{ selections} \]

Each selection of five letters can be arranged in

\[ 5! = 120 \text{ ways} \]

\[ 210 \times 120 = 25{,}200 \]

A "word" is an ordered string, so the arrangement step is essential; stopping at 210 counts only which letters are used.

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