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) if there are no restrictions does that mean its 10! or since there are repeated letter it would be 10!/3!2!2! ?
b)8*8! ?
c) (3) * (7!/3!2!) ?

Answer 1

a) Because of repeated letters: 10! / (3!2!2!)

Answer 2

ok thats what I thought.

Answer 3

For b) treat EE as one entity. In how many permutations will EE occur consecutively. Then subtract this from the total number of permutations.

Answer 4

umm. if EE is one entity then it can go in 1 of 9 spots?

Answer 5

so 10!/(3!2!2!) - 9??

Answer 6

STATEMENTS
If EE is treated as one entity, we have (EE)SSTTTAMN
Now there are 9 entities that can be permuted in 9! ways. But since there are two Ss and 3 T's, the number of distinct permutations is: 9! / (3!2!).
The number of distinct permutations in which EE occurs consecutively is 9! / (3!2!).

Number of permutations where EE does not occur consecutively is:
10! / (3!2!2!) - 9! / (3!2!).