# Combinations: combinations vs permutations in particular exercise

I am confused by the following exercise. First, I will present the exercise with solution, after that there is a problem that I have about this exercise.

Exercise. From 7 consonants and 5 vowels, how many words can be formed consisting of 4 different consonants and 3 different vowels? The words need not have meaning.

Solution. The 4 different consonants can be selected in $_{7}C_{4}$ ways, the 3 different vowels can be selected in $_{5}C_{3}$ ways, and the resulting 7 different letters (4 consonants, 3 vowels) can then be arranged among themselves in $_{7}P_{7}$ - $7!$ ways. Then Number of words - $_{7}C_{4}$ $_{5}C_{3} 7! = 1,764,000$.