## anonymous one year ago Probability assistance for a medal, anyone? Suppose you select 2 letters at random from the word compute. Find each probability. P(2 vowels) Side note: In the video I watched on this topic, the guy used a calculator that supported nCr, but I cannot find one that can solve this problem.

1. anonymous

I know the equation to solve this is $\frac{ s }{ s+f }$ s = successes and f = failures I'm not sure how to get an answer though.

2. anonymous

There are $$7$$ letters you can choose from the word "compute". $$3$$ of these are vowels (o,u,e). There are $$\dbinom72={}_7C_{2}=\dfrac{7!}{2!(7-2)!}$$ ways of choosing any $$2$$ letters, and $$\dbinom32\times\dbinom40=\dfrac{3!}{2!(3-2)!}\times1$$ ways of choosing two vowels. So, $P(\text{2 vowels})=\frac{\dbinom32}{\dbinom72}$

3. anonymous

Thank you for your help. :)