How many sets of 10 can you get from 20?

Answer 1

Many sets of 10 different people can be selected from a group of 20 different people.

Look at it this way: Imagine the sets of 10 and 20 are people. Then the people we choose for the first set of 10 can be arranged in any order. In other words the order does not matter.

Having chosen the 10 to make the first set we have 10 people "left over". Now each one of those left over can be exchanged for one in the first set, so there are 10 ways of "swapping" the first one.

But for each of these 10 ways there are 9 ways of swapping the second member from those still left over. So there are 10 x 9 ways of doing that. Similarly there will be 8 ways of swapping the third member, which means there are 10 x 9 x 8 ways of doing that.

If we continue swapping until all 10 of those not in the original first set have replaced someone who was in the first set, then there are 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 ways of choosing a set of 10 from the 20.

That is 3,628,800 different sets of 10. Unbelievable but true. Over three and a half million.

If you could move the people so quickly that you could make a new set of 10 every minute it would take 6 years and 330 days - and that would be using every minute of the day (no sleep).