Question

Discrete random variables - Binomial distribution

I don't understand how to answer question (c) in the attached image.

Answer 1

Hints:
"For (a) use the same thought process as in the question's preamble about the UK lottery.

For (b) imagine that there is a card for every one of the subsets of 7 numbers. As 48-7= 41 of the numbers will be 'losers', how many subsets of 7 'losers' can be formed. Find what proportion these are of all the subsets of size 7, and you have the required probability.

For part (c) the proportional reasoning is the same. But you have to count the number of subsets with one winner and 6 'losers'. Suppose you pick on one of the winning numbers. Then how many subsets with 6 'losers' are there? Then choose a different winning number and consider again how many subsets of 6 losers there are. So in total there are how many subsets that have exactly one winning card?"