1. ## Probability Question

There are 6 letters, A-F. The GRE booklet problem involves arranging them in groups of 3. I already know the formula for this: n! divided by (n)(n-1). You get 20. But the question in my book asks how many of the groups of 3 contain the letter F. How does one figure that out with a formula instead of writing them all out? Thanks in advance.

2. ## Combinatorics

Hello GREhelp
Originally Posted by GREhelp
There are 6 letters, A-F. The GRE booklet problem involves arranging them in groups of 3. I already know the formula for this: n! divided by (n)(n-1). You get 20. But the question in my book asks how many of the groups of 3 contain the letter F. How does one figure that out with a formula instead of writing them all out? Thanks in advance.
I'm not quite sure where you arrive at $\frac{n!}{n(n-1)}$. This gives $(n-2)!$, which is $24$ if $n = 6$.

(a) How many groups of 3 can we choose from 6 items? Answer: $\binom{6}{3}=\frac{6!}{3!3!}= 20$.

(b) How many groups of 3 contain the letter F? Answer: the same as the number of ways of choosing the other 2 letters from 5, which is $\binom{5}{2}= \frac{5!}{2!3!}= 10$.