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How many 5-letter words, each with 3 different consonants and 2 different vowels, can be formed from 7 consonants and 4 vowels?

Competition practicePermutations & Combinations

A12600
B25200
C210
D50400

Step-by-Step Solution

Choose:

^{7} C_{3} \times^{4} C_{2} = 35 \times 6 = 210

. Arrange each choice of 5 letters:

5! = 120

. Total

210 \times 120 = 25200

. (210 forgets to arrange.)

Answer: B) 25200

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