These are straight Combinations questions.
Exactly where is your difficulty?
possible winning combinations.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.
The lottery pays off if you match 5, 4, or 3 of the numbers.
a) How many different winning number combinations are there?
b) What is the probability that you will match all 5 of the winning numbers?
There are: . ways to match 4 numbers.c) What is the probability that you will match exactly 4 of the 5 winning numbers?
Your 5th number is from the other 40 non-winners: . ways.
. . Hence, there are: . ways to match exactly 4 numbers.