Question

how many ways can the word STATEMENTS be rearranged?

a) with no restrictions
b)with no consecutive E's
c)with all vowels consecutively

my attempt.
a) 10!/3!2!2! ?
b)10!/(3!2!2!) - 9 ??
c) (3) * (7!/3!2!) ?

Answer 1

a looks good
b should be (10*9/2 - 9)*8!/(3!*2!)
(10*9/2 - 9) is the number of ways to place the two E's nonconsecutively
8!/(3!*2!) is the number of ways to place the rest of letters, once the E's are placed

Answer 2

oh ok great thanks. what about c?

Answer 3

(3*8)*7!/(3!*2!)
3*8 is the number of ways to place vowels consecutively
7!/(3!*2!) is the number of ways to place the rest of the letters

Answer 4

ok I was only missing the 8 different spots to put the vowels. thanks alot