For a particular lottery, the winning numbers are selected by a machine that randomly chooses 5 table-tennis balls from among 45, numbered 1 to 45.
What is the probability that you will match exactly 4 of the 5 winning numbers ?
If so, then the answer would agree with an alternate approach I tried:
Without loss of generality, we can suppose that the balls numbered 1 through 5 were randomly chosen, and we want the probability that exactly four match.
The above is to illustrate that there are 40*5 combinations for which exactly four match, so the probability is given by 40*5/C(45,5).
there are ways to choose 4 of the 5 winning numbers.
The selection of 5 must contain one of the 40 remaining numbers,
hence there are ways to match 4.
There are ways to choose 5 from 45
so the probability of matching 4 of the 5 winning numbers with a single selection is