Multiple choice

Four-letter words are formed using 17 consonants and 5 vowels. How many will have 2 different vowels in the middle and a consonant at each end?

  1. 5780

  2. 5440

  3. 6700

  4. 7225
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B Correct answer
Explanation

To form the four-letter word with different letters, we need to place two different vowels in the middle and two different consonants at the ends. The number of ways to choose and arrange 2 different vowels from 5 is 5 * 4 = 20. The number of ways to choose and arrange 2 different consonants from 17 for the ends is 17 * 16 = 272. Multiplying these gives 20 * 272 = 5440 words.

AI explanation

To form the required word, select and arrange one consonant for each end using the permutation formula 17P2, which equals 17 times 16, or 272. Next, select and arrange two different vowels for the two middle positions using 5P2, which equals 5 times 4, or 20. Multiply these independent arrangements to find the total number of words: 272 times 20 equals 5440.

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