Question

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.

Answer 1

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.

Answer 2

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,
\[P(\text{2 vowels})=\frac{\dbinom32}{\dbinom72}\]

Answer 3

Thank you for your help. :)