How many ways can a committee of 4 people be chosen from 10 people?

Either 5040 or 210, depending on a whether order is important. Keep reading.

Four slots. First slot: 10 people to choose from 2nd slot: 9 people left (1 is already chosen) 3rd: 8 4th: 7

10*9*8*7=5040, assuming, of course, the people are chosen randomly and no one person can be on the committee twice.

But then we need to adjust this figure because there will be some duplication, since if Ben, George, Sue, and Jill are chosen for example, there are different ways that they can be chosen and all four of these same people are still on the committee. This is much like when Lotto balls are draw - you don't really care what order the balls are drawn as long as you match them up. So the number of ways that 4 people can be arranged in 4 positions is 4! = 4 x 3 x 2 x 1 = 24. So dividing 5040 by 24 will give you the number of possible committee selections, assuming that it doesn't matter which order they are chosen.