How many three-letter arrangements can be made from the letters in MOUSEPAD if no letter can be used more than once and each arrangement is made up of a vowel between two consonants?

Vowels A , E , O , U

Consonants D M P S

Choose any 1 of the 4 vowels = C(4,1) = 4

Choose any 2 of the 4 consonants and permute them in 2 ways = P (4,2) = 12

Total arrangements = 4 * 12 = 48

Thank you so much!