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How many different ways can 5 people be selected from a group of 18?
The number of ways is 18C5 = 18!/(5!*13!) = 8,568 ways.
Given the digits 0-9... how many ways can you form an even number without replacement of numbers?
one digit: 5 ways two digits: 5 * 9 ways three digits: 5 * 9 * 8 ways four digits: 5 * 9 * 8 * 7 ways ... ten digits: 5 * 9! ways So if you have to use ten digits, then the answer is 5 * 9! = 1814400. If you can use anywhere from one to ten digits, then the answer is: 5 * (9! + 8! + 7! + 6! + 5! + 4! + 3! + 2! + 1) = 2045565
How many ways can you arrange 14 people in a row?
87,178,291,200 ways. That is factorial 14 or expressed as 14! = 14*13*12*10*9*8*7*6*5*4*3*2*1 With just 4 people there are 4*3*2*1 = 24 ways With 5 people there are 5*4*3*2*1 = 120 ways etc.etc.
How many ways can 8 people sit in 5 chairs?
8x7x6x5x4= 6720
How many ways can 5 people sit in a row if 2 of them insist on not sitting together?
The first thing to do is to work out how many ways there are without those 2 people minding. There are 5 possibilities for first place, 4 for second and so on, so the number of ways is 5x4x3x2x1 = 120. The next step is to work out how many of these possibilities have the two people sitting next to each other. There are 4 ways in which two people can sit next to each other. For each of these ways there are two possibilities, one with one person on the right, and the other with them on the left. For each of these 8 ways, there are 3x2x1=6 ways the other people could have sat. So there are 8x6=48 invalid ways in total. 120-48 = 72 So there are 72 ways 5 people can sit in a row if 2 of them insist on not sitting together.
