Math Help - Permutation Help!

1. Permutation Help!

Consider the Permutations of the word SUCCESSFUL ?

a) How many permutations total?
b)How many have the 3 vowels adjacent (such as SUUESSFCLC)?
c)How many permuations have none of the 3 vowels adjacent?
d)How many permutations start with an S and end with an L?
e)How many permutations have a consonant as the first letter?

2. Originally Posted by zackgilbey
Consider the Permutations of the word SUCCESSFUL ?
a) How many permutations total?
$\frac {10!} {(3!)(2!)(2!)}$
Now you do some work. Show us some work.

3. im plugging away at this, and i understand the 10 factorial as well as the (2!) (2!), but not positive on how the 3! was determined. thanks

4. Originally Posted by zackgilbey
im plugging away at this, and i understand the 10 factorial as well as the (2!) (2!), but not positive on how the 3! was determined. thanks
Surely this topic is included in your text material: arrangements with repetitions.
The number of ways to rearrange the word “MISSISSIPPI” is $\frac {11!}{(4!)^2(2!)}$.
That is due to the fact there are 11 letters in all, 4 S’s, 4 I’s, and 2 P’s.
Consider the word “UNUSUAL”. There are there are seven letters in all.
If we add subscripts $U_1NU_2SU_3AL$, now the number of ways to rearrange the word is $7!$.
But removing the subscripts makes us divide $3!$ to account for the fact that is the number of ways to rearrange $U_1U_2U_3$.

5. thanks for the help ive been able to plug right through these except the last one e) im having trouble with how to approach this one as I havent seen this type of question before... any help regarding this would be excellent thanks