b) These are the consonants are: P,R,B,B,L,T,S.

They can be arranged in ways;

Each of the ways creates 8 places _P_R_B_B_L_T_S_ to put the vowels.

The number of places is then . The number of vowel arrangements is

Put it together: .

a) “PROBABILITIES” the word has 13 letters but some repeat.

There are ways to arrange this word: 3 I’s & 2 B’s.

You now must find the number of ways we can have “EI”, “IE”, or “IEI”

And subtract from total.