HELP ME PLEASE

Question

a box of jawbreakers contains 4 blue, 2 red, 6 green, 1 purple, and 2 yellow jawbreakers. if randomly selects 5 jawbreakers, what is the probability he gets exactly 3 the same color?

Answer 1

This is not an easy problem. With many of these types of probability problems, it helps to remember the universal formala for calculating probability - that it is the ratio of the desired outcomes (a numerator) divided by all possible outcomes (denominator). The easy part here is the denominator - total possible outcomes - which should be 15 factorial (or 15!). Since there are 15 total jawbreakers, there are 15 possible choices for the first, then 14 for the 2nd, etc.

 

Now, for the numerator - there are only 2 ways to get 3 of the same color - either all blue, or all green, but there are 4 blues, and 6 greens, so you must be careful. Ask yourself - How many ways are there to get all blues? Well, since there are 4 blue ones, there are 4*3*2*12*11, I think. That is because there are 4 choices for the first blue one, then 3 for the 2nd, then only 2 for the 3rd, but then for the other 2 choices (to get to 5 total), there are 12 remaining jaw breakers, so you have to multiply by 12*11 also for the 4th and 5th choices. Note that the order of selection is not important, only the outcome of picking 5 jawbreakers out of 15 choices.

 

Now do the same thing for the green - there are 6*5*4*12*11 ways to pull 3 greens. Now you must total all choices together (blues + greens) to get your numerator, then divide by the total possible outcomes (15!).

 

Hope I did that right.

 

- Ben