Why is the answer that they are the same. I saw Greg’s explanation on this but when I try to prove his explanation right I get the following for A: (5/10)(4/9)(3/8)(2/7)(5/6) which is different than B: (5/10)(4/9)(3/8)(2/7)(1/6)(5/5). If you cancel out the first four fractions on both sides you are left with comparing (5/6) with (1/6) which are obviously not the same. What am I missing? Thank you!
Because for every arrangement (of 10 marbles that are picked out) with red as the fifth pull, you can imagine swapping the fifth and sixth element so as to have an equal number of arrangements with red as the sixth pull.
Naturally then the answer is that they’re the same.
You’re only considering one specific case. For example, for quantity A you’re considering a case where all your first five marbles are red (RRRRR). What about cases like GRGRR, GGGGR, and other cases of this sort?
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You can also treat this is as a basic combinatorics exercise in which you count how many arrangements (with 10 marbles) have red in the 5th (or any nth) position (if we treat each red and green marble as distinct). You should have something like:
\frac{9!}{10!} = \frac 1{10}
Since all 5 red marbles are the same, then you have 5 \cdot \frac {1}{10} = \frac 12
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