Vegita wrote:
KarishmaBFirst of all, thank you for your reply.
Assuming our sample size is just this below.
H1, W1, H2, W2, H3, W3
For the first step, if I do 6C1 to select 1st person then this will ensure that I pick anyone. Let's say I picked H1.
For the second step, if I do 4C1 to select the 2nd person, considering that I am taking in my sample size H2, W2, H3, W3, and NOT W1.
Wouldn't the second step ensure that the other partner is not selected?
When you select one after another without replacement from the same set, you run the risk of double counting.
Consider
H1, W1, H2, W2, H3, W3 - say you need to select 2 people such that they are not a couple.
You do 6C1 and select H2 say.
Now you ignore W2 and select 1 out of the remaining 4 in 4C1 ways. You select W3 say.
You get H2, W3 as your selection.
Consider that at some point, when you select 6C1, you will get W3 first. Then you will ignore H3 and select 1 of the remaining 4. In one case, you will select H2.
So you again get H2, W3 as your selection since there is no arrangement.
You will end up double counting this selection. So you need to divide the total number of cases by 2! so un-arrange.
Similarly, in the case of selecting 3 out of 10, you can use 10C1 * 8C1 * 6C1 but you need to divide by 3! to un-arrange. This is the approach that has already been discussed.
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Karishma
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23 Apr 2022, 07:28
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