You have 50 ways to select the first.
For each of those 50, you have 49 ways to select the second.
Only 49 ways, because for each of the 50, there are only 49 left to select from.
That's 50 x 49 ways to select the first and the second.
For each of those 50 x 49 ways, you have 48 ways to select the third.
That's 50 x 49 x 48 ways to select the first, second and third.
For each of those 50 x 49 x 48 ways, you have 47 ways to select the fourth.
That's 50 x 49 x 48 x 47 ways to select the first, second and third and fourth.
But if it doesn't matter what order they are selected in, the same four people have been counted multiple times. For example, if people A, B, C and D have been selected, we will have counted A, B, C and D as one way, and D, C, B and A as another, B, D, A and D as another. In fact, there are 4 x 3 x 2 x 1 ways of counting any four people.
So if order does not matter, there are (50 x 49 x 48 x 47) / (4 x 3 x 2 x 1) ways.
How many ways can 5 finalists be selected from 100 people?
The number of ways is 18C5 = 18!/(5!*13!) = 8,568 ways.
There are 8!/(4!*4!) = 70 ways.
30 = 6 * 5 if we assume the president and the vice-president must be different people.
-5
3 people can be selected from a pool of 7 people in (7 x 6 x 5) = 210 ways.But each group of 3 can be selected and seated in (3 x 2 x 1) = 6 ways.So the number of different 3-person subcommittees formed from 7 people is (210/6) = 35 .
The number of ways is 18C5 = 18!/(5!*13!) = 8,568 ways.
There are 8!/(4!*4!) = 70 ways.
In how many ways can fourfour women be selected from the eighteight ​women
They can be selected in 756 ways.
If there are 58 defective circuit boards, two can be selected in 58*57/2 = 1653 ways.
There are 14C8 = 14*13*12*11*10*9/(6*5*4*3*2*1) = 3003 ways.
18x17= 306 ways
53,130 ways.
35
30240
The number of ways is 10C5 = 10!/(5!*5!) = 10*9*8*7*6/(5*4*3*2*1) = 252
560.