# Probability Question

• sam_0017

#### sam_0017

can anyone help me with this Question ?

On a TV Game Show fifteen people from the audience are chosen randomly to compete
for prizes. Assume these fifteen people return in the audience of N people for the next
week's show when another fifteen people are chosen randomly to compete for prizes.
(i) How many possibilities are there to choose 10 people out of the 15 people?
(ii) How many possibilities are there to choose 15 people out of the audience of N
people?
(iii) Write an expression for the probability that exactly 10 of the 15 people from
the first show are again chosen to compete for prizes in the week after.
(Hint: Imagine the situation as follows: we first choose 10 people out of our 15
people and then the remaining 5 people out of the rest of the audience. To find
the probability, compare the number of possibilities to proceed in this way with
the number of possibilities of choosing 15 arbitrary people out of the total
audience.)
(iv) What is the minimum value N must be so that it is possible for the event in (iii)
to occur?

This is homework right? Presumably you have just completed some lessons on combinations and permutations? For this you have some notes? The answers are in your notes.

For example:
The number of different ways I can choose 5 people out of a group of five ... I can pick any of the five for the first spot, any of the remaining four for the second slot and so on, for a total of 5x4x3x2x1=120 different ways. (But if the order doesn't matter there is only one way.)

If I only have three spots to fill, there would be 5x4x3=60 different ways to do this.

Your notes will probably use special notation that you are expected to learn. Probably something like these:
http://en.wikipedia.org/wiki/Permutation
http://en.wikipedia.org/wiki/Combination

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https://www.amazon.com/dp/0809058405/?tag=pfamazon01-20
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