# Permutation of theory

• May 18th 2008, 05:15 PM
Jigglypuff
Permutation of theory
Each permutation of the letters in THEORY is written on a slip of paper and tossed into a bowl. One slip is drawn at random, what is the probability that the letter T willappear in the last position?
• May 18th 2008, 05:31 PM
Unenlightened
Quote:

Originally Posted by Jigglypuff
Each permutation of the letters in THEORY is written on a slip of paper and tossed into a bowl. One slip is drawn at random, what is the probability that the letter T willappear in the last position?

THEORY... Six letters.
Only one can come last at any given time.
There's a one in six chance that this will be 'T'.
So: 1/6.
That's probably the simplest way of looking at it...

You could also say that you had:
5/6 * 4/5 * 3/4 * 2/3 * 1/2 * 1/1 = 1/6.

I think...
• May 18th 2008, 07:59 PM
Soroban
Hello, Jigglypuff!

Yet another approach . . .

Quote:

Each permutation of the letters in $THEORY$ is written on a slip of paper
and tossed into a bowl. One slip is drawn at random.
What is the probability that the letter $T$ will appear in the last position?

There are $6! = 720$ permutations of the six letters.
. . Hence, there are 720 slips of paper in the bowl.

If $T$ is last: . $\_\:\_\:\_\:\_\:\_\:T$
. . the other 5 letters can be arranged in $5! = 120$ ways.
Hence, there are 120 slips with $T$ in the last position.

Therefore: . $P(\text{ T is last }) \;=\;\frac{120}{720} \;=\;\boxed{\frac{1}{6}}$