Probability of Drawing 5 and 6 from a Box with Numbered Discs | Combinatorics

[Larrytsai]

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 I am not getting the correct answer, and i also tried
P(A/B)= P( A&B)/ P(B)

 

[rock.freak667]

So you want to get 5 and 6

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

 

[Larrytsai]

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

 

[Dick]

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

 

[Larrytsai]

there are 10C2 ways which equal =45

 

[Dick]

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

 

[diazona]

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]

Or: there is a 2/10= 1/5 probability of getting either 5 or 6 on the first disc. Having done that, there are now 9 disks left, one of which has the other (6 or 5) so there is a 1/9 probability of drawing that one. Together, there is a (1/5)(1/9)= 1/45 probability of drawing 5 and 6 in either order.