The number of 4-letter words formed from the English alphabet such that there are exactly 2 vowels and 2 consonants and no vowel is repeated, but consonants may be repeated is:

Step-by-step solution

The 4-letter word requires exactly 2 vowels and 2 consonants. The number of ways to choose 2 positions out of 4 for the vowels is ⁴C₂ . Since no vowel is repeated, the number of ways to choose and arrange 2 distinct vowels from the 5 available vowels in the chosen positions is ⁵P₂ . The remaining 2 positions must be filled with consonants. Since there are 21 consonants and repetition is allowed, each position can be filled in 21 ways. The number of ways to fill the consonant positions is 21 21 = (21)^2 . The total