# Probability Question

Ten discs numbered 0 to 9 are placed in a box. Two discs are randomly removed without replacement. Determine the probability that one disc will have the digit 5 written on it, and the other disc will have 6 written on it.

I tried cominatorics to do this question but im not getting the correct answer, and i also tried
P(A/B)= P( A&B)/ P(B)

rock.freak667
Homework Helper
So you want to get 5 and 6

P(5&6)= P(5)*P(6)

ummm that gives me 1/90 which is not the correct answer :|

Dick
Homework Helper
You want to pull two special disks from a collection of 10 disks. How many ways are there to pull two disks?

there are 10C2 ways which equal =45

Dick
Homework Helper
Right. Only one of those 45 ways will give you 5 and 6.

diazona
Homework Helper
So you want to get 5 and 6

P(5&6)= P(5)*P(6)
If you're going to do it that way, you need to consider the probability of getting 6 followed by 5, as well as the probability of getting 5 followed by 6. So it's really
P(5,6) = P(5)*P(6) + P(6)*P(5) = 1/90 + 1/90 = 1/45
same answer you get from combinatorics ;-)

HallsofIvy