# Permutation Help!

• Jan 16th 2009, 01:33 PM
zackgilbey
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?
• Jan 16th 2009, 01:41 PM
Plato
Quote:

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.
• Jan 16th 2009, 02:43 PM
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
• Jan 16th 2009, 03:12 PM
Plato
Quote:

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 $U_1U_2U_3$.
• Jan 18th 2009, 10:47 PM
zackgilbey
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