How many ways can we rearrange the letters of the word FACIAL so that no rearrangements start with vowels? The two A's are indistinguishable.

(Plz help fast)

NerdyWeeb Aug 18, 2020

#1**0 **

There are: 6! / 2! =360 permutations for "FACIAL". Each of the 360 permutations begins with one of the 6 letters in FACIAL: 360 / 6 =60 permutations beginning with each letter. Since you have 2 "A", therefore, there will be:60 x 2 =120 permutation beginning with the letter "A". And since there is only one "I", there will be 60 permutations beginning with the letter "I".

So, 360 - 120 - 60 =180 permutations that will NOT begin with a "vowel"

Guest Aug 18, 2020