In a new provincial weekly lottery you must select 4 numbers

In a new provincial weekly lottery, you must select 4 numbers (in any order) correctly out of a possible 30 numbers to win the one and only top prize. If you purchase one ticket (with your four numbers on it) this week, what is the probability of winning the top prize? Keep your final answer to six decimals. Fifty cyclists compete in a national championship bike race. How many ways can the cyclists finish first, second, and third?

Solution

NOTE : we are suppose to answer one question at a time. i will give you the answer for 2nd for rest repost the question.

In a 50 man race, how many cyclist have the chance to finish first?
answer 50.
Now that 1 person is first, how many runners could be second? Well, there are still 49 cyclist left, and any one of hem could be second.
Answer 49.

How many can be third? Using the same idea as above, once one person is first and another is is second, that leaves 48 people still cycling and trying for third. So how many can be in third?
Answer 48.
Now you need to do the math
50*49*48
So there are 117600 different ways.