Multiple choice

From a collection of 7 unique consonants and 5 unique vowels for a creative writing contest, how many distinct 6-letter titles can be formed such that each title consists of 4 consonants and 2 vowels?

  1. 125,120

  2. 225,000

  3. 252,000

  4. 283,000

  5. 382,000
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Choose 4 consonants from 7: 7C4 = 35. Choose 2 vowels from 5: 5C2 = 10. Total combinations = 35 * 10 = 350. Arrange 6 letters: 6! = 720. Total = 350 * 720 = 252,000.

AI explanation

Selecting 4 consonants out of 7 and 2 vowels out of 5 can be done using the combination formula in 7C4 and 5C2 ways, respectively. This gives 7C4 = 35 ways and 5C2 = 10 ways, yielding 350 possible sets of 6 letters. Since each set of 6 distinct letters can be arranged in 6! = 720 ways, the total number of titles is 350 multiplied by 720, which equals 252,000.

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