arjun.malhotra wrote:Out of curiosity, the way I attempted to solve this was through chain. Though I seem to have erred right at the end.

3x chains,

J or H (assume J) * H * Other (i)

Other, J or H , H (ii)

J or H , Other, H (iii)

2/5 * 1/4 * 3/3 = 6/60

3/5 * 2/5 * 1/5 = 6/60

2/5 * 3/4 * 1/3 = 6/60

added = 18/60 = 3/10 (as per answ in book)

The mistake I made was to multiply each chain by 2, as there are two possibilities for order in each of the above chains,

So on chain (i) J or H (assume J), H, Other OR J or H (assume H), J, Other

Hence (6/60*2)*3 which led to the original answer I got, 3/5

Is there any reason why order H, J or J, H along the same probability chain does not matter here as it does in the answer solution where chance of success is broken down so as to identify each actress individually, 1/5 * 1/4 instead of probability of 'success', selecting either one of them 2/5 * 1/4.

Thank you

Hi arjun,

It appears that you've identified something important here, which is that order does NOT matter. We just need to have combinations of J, H, and someone else. I don't care of J is picked first for the movie, if H is picked first, or if the third member of the group is picked first. I need all three together as a group.

You are right that multiplying 1/5 * 1/4 * 1 gives the probability of a particular order. By doing that I'm using the slot method:

1/5 chance of picking Julia

(I pick Julia. Four people are left)

1/4 chance of picking Halle

(I pick Halle. Three people are left)

3/3 chance of picking a third person (we don't care about who this is)

1/5 *

1/4 *

1 = 1/20

When you use the slot method you are assuming that order matters, and the slot method does give you the probability of a specific order. What if I want to use the slot method but order actually does NOT matter? If that's the case, I need to adjust my number of outcomes. I do that by multiplying the result by the factorial of the number of slots. In this case I have three slots, so I multiply by 3!, or 6. Thus 1/20 * 6 = 3/10, the answer.

I hope that this makes more sense. Please let us know if you have more questions.