Statistics/probability?

A box contains 5 white tags numbered 1 to 5, 5 red tags numbered from 1 to 5, and 5 green tags numbered from 1 to 5. If two tags are selected at random and without replacement what is the probability that:





a) both are the same number?


b) both are the same color?


c) they are consecutive numbers but of different colors?


d) they are consecutive numbers of the same color?








If you could please explain in more detail, I'd really appreciate it!

Statistics/probability?
First, the total number of combinations is actually 15 choose 2 = 15*14/2*1 = 105, since the order in which you pick them doesn't matter.


a) There are three ways to pick two 1s: red and green, red and white, or green and white, for 3 possibilities. Likewise there are 3 possibilities for 2s, 3s, 4s, and 5s, so that gives 15 ways to pick two of the same number; thus the probability is 15/105 = 1/7.


Another way to see this is this: after you pick the first tag, 2 of the 14 remaining tags match its number. Thus the probability that the second one matches is 2/14=1/7.


b) How many combinations of two red tags are there? 5 choose 2 = 10. (R1R2, R1R3, R1R4, R1R5, R2R3,...) There are also 10 combinations of two green tags and 10 of two white tags, so that gives 30/105 = 2/7.


Again, we can also see this by pulling the first tag and realizing that 4 out of the remaining 14 tags match in color, so the probability must be 4/14=2/7.


c) This one is a little harder. How many ways can you pull a 1 and a 2 of two different colors? They can be RG, RW, GR, GW, WR, or WG, so that's 6 combinations. Likewise for a 2 and a 3, 3 and a 4, or 4 and 5...each have 6 combinations. That's 24 total combinations, so the chances are 24/105=8/35.


d) This one is easier to count: we can get R1R2, R2R3, R3R4, or R4R5 in red for 4 combinations. Counting 4 more for green and 4 more for white gives 12 total combinations, for a probability of 12/105=4/35.
Reply:There are C = 15 x 14 = 210 possible combinations.





a) 5 x 2 = 10, so 10/210 or 4.76%





The first one can be any number 1-5. The second one must be the same number but of a different color (there are only two possibilities).





b) 3 x (5)(4) = 60, so 60/210 or 28.57%





The first one can be any number 1-5. The second one must be the same color (there are four left). And there are three colors.





c) 3 x (4)(2) = 24, so 24/210 or 11.43%





The first one can be only 1-4. The second one must be a specific number of a different color (there are two of these possible). There are three colors.





d) 3 x (4)(1) = 12, so 12/210 or 5.71%





The first one can be only 1-4. The second one must be the next number in the same color (there is only one possibility). There are three colors.