Name: Yvonne

Who is asking: Teacher Level: Secondary

Question:
What is the probability of 38 people choosing the same five options, given a choice of 15?

Perhaps you could just give me the formula with an explanation.

I am an English teacher doing educctional research, but am stuck because I don't have the math experience to help me.

Thank you, Yvonne



Hi Yvonne,

We are not exactly sure what the question is so let me first describe what I think it is. You have 38 subjects in your study and each is given the same 15 options and asked to choose 5. I think your question is then "What is the probability that each iof the 38 subjects chooses the same 5 options?" If this is the question then we can solve it in the following way.

In how many ways can we choose 5 from 15. These are combinations

C[15,5]=(15!)/(10! * 5!)= 3003. Now, for one person to choose the fixed 5 options the probability is  1/3003. We have 38 subjects, so the first one can choose whatever she/he wants. All other 37 have to choose the same options, so the answer is ( 1/3003) 37, which is very close to zero.

Andrei

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