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02 Sep 2025, 07:37
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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A special language is invented with 12 consonants and five vowels. All words in the language contain exactly four letters. All words begin and end with a consonant and have two vowels in between. How many possible words in the language contain four different letters?
21 Sep 2025, 04:20
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Official Explanation
Draw out four blanks to represent the four places in the word to be filled: ________ ________ ________ ________. In each blank, write the number of different ways that particular place can be filled. The total number of combinations will then equal the product of the numbers in the blanks. There are 12 consonants and five vowels in the language. Words fit the CVVC pattern, so we might expect the total number of possible words to equal 12 × 5 × 5 × 12. But since we are looking for words with no repeated letters, the number of possibilities for the second vowel and for the second consonant are each reduced by 1, so the answer becomes 12 × 5 × 4 × 11 = 2,640 possible words with four different letters.
Answer: 2640
Draw out four blanks to represent the four places in the word to be filled: ________ ________ ________ ________. In each blank, write the number of different ways that particular place can be filled. The total number of combinations will then equal the product of the numbers in the blanks. There are 12 consonants and five vowels in the language. Words fit the CVVC pattern, so we might expect the total number of possible words to equal 12 × 5 × 5 × 12. But since we are looking for words with no repeated letters, the number of possibilities for the second vowel and for the second consonant are each reduced by 1, so the answer becomes 12 × 5 × 4 × 11 = 2,640 possible words with four different letters.
Answer: 2640
