Question

There are 15 people to choose from and 4 places to put them in. How many of the groups include Bob? (This is probability. I made up the problem because I don’t know how to do this and I have a test 4th hour!)

Answer 1

If we absolutely want Bob in the group, then there are 3 remaining places to fill, and 14 people to choose from. The number of groups is then


`\dbinom{14}3=(14!)/(3!(14-3)!)=(14!)/(3!11!)=(14\cdot13\cdot12)/(3!)=364`