You can pull 4 people out of the crowd in (50 x 49 x 48) = 117,600 ways.
But you'll find that every group of 4 people has been pulled in 24 different ways
at 24 different times during the selection process.
The number of different groups of 4 finalists is (50 x 49 x 48)/(4 x 3 x 2) = 117,600/24 = only 4,900.
If order matters, 50x49x48x47 = 5,527,200. If the order doesn't matter (which it probably doesn't, given that we're not selecting the winner, first runner-up, etc. directly), it's slightly trickier: there are 4!, or 24, ways of arranging four items, so we have to divide the larger number by 24 to get 230,300.
In how many ways can fourfour women be selected from the eighteight ​women
They can be selected in 756 ways.
42
If there are 58 defective circuit boards, two can be selected in 58*57/2 = 1653 ways.
18x17= 306 ways
53,130 ways.
There are 1,235,520 ways.
30240
35
The number of ways is 18C5 = 18!/(5!*13!) = 8,568 ways.
Since the three prizes are the same, the answer is the number of combinations of 3 out of 80. That is 82160 ways.