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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?