1. permutation question

if you have the letters A,B,C,D,E and you form 3 letter "words" with these letters, what is the probability that the word starts with D?

how do I show this using permutations?

using fractions I know the answer is $\displaystyle \frac{1}{5}$ (1/5 *4/4*3/3)

so it would be $\displaystyle \frac{something}{_{5}P_{3}}$

how do I show the number of possible combinations that begin with D as a permutation?

2. Originally Posted by hello
if you have the letters A,B,C,D,E and you form 3 letter "words" with these letters, what is the probability that the word starts with D?
I assume that you mean three different letters.
There are $\displaystyle (5)(4)(3)=60$ possible three letter words.
There are $\displaystyle D(4)(3)=12$ that begin with D.

3. Originally Posted by Plato
I assume that you mean three different letters.
There are $\displaystyle (5)(4)(3)=60$ possible three letter words.
There are $\displaystyle D(4)(3)=12$ that begin with D.
thus the probability of making a word that begins with D is $\displaystyle \frac{12}{60}$

how do I show this using permutations, though?

$\displaystyle \frac{possibilities with D as first letter}{_{5}P_{3}}$

I know the numerator is 12 since $\displaystyle _{5}P_{3}$ = 60

I just need to use another permutation for the numerator. Sorry if my OP was confusing

4. Originally Posted by hello
thus the probability of making a word that begins with D is $\displaystyle \frac{12}{60}$ YES
I just need to use another permutation for the numerator.
Because D has be used, you have $\displaystyle _4 P_2 =12$

5. Ah ok. Thanks