SOLUTION: A technician is launching fireworks near the end of a show. Of the remaining thirteen fireworks, seven are blue and six are red. If she launches six of them in a random order, what

Question 1106683: A technician is launching fireworks near the end of a show. Of the remaining thirteen fireworks, seven are blue and six are red. If she launches six of them in a random order, what is the probability that exactly two of them are blue ones?
Hi, I have attempted this question multiple times and while I get the total number of ways she can select 6 out of 13 (1716)
My answer does not match the textbook's for the number of ways she can get 2 out of 6. The correct answer is supposed to be 105/572 but I get 75/572
I would really appreciate the help, thanks so much
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Note that we would be in a much better position to tell you why you are getting the wrong answer if you SHOWED us how you got it....

You want 2 of the 6 she chooses to be blue, which means 4 are red. There are 7 blue and 6 red remaining.

She is choosing 6 of the remaining 13 fireworks; the number of ways she can do that is "13 choose 6".

You want the probability that of those 6, 2 are blue and 4 are red. So she needs to choose 2 of the 7 remaining blue fireworks (7 choose 2) and 4 of the remaining 6 red fireworks (6 choose 4).

So the calculation should be straightforward:

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