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Consider a group of 20 people. If everyone shakes hands with everyone else, how many handshakes take place?

How many 5 -card poker hands are there?

A student has to sell 2 books from a collection of 6 math, 7 science, and 4 economics books. How many choices are possible if (a) both books are to be on the same subject? (b) the books are to be on different subjects?

Seven different gifts are to be distributed among 10 children. How many distinct results are possible if no child is to receive more than one gift?

A person has 8 friends, of whom 5 will be invited to a party. (a) How many choices are there if 2 of the friends are feuding and will not attend together? (b) How many choices if 2 of the friends will only attend together?

The game of bridge is played by 4 players, each of whom is dealt 13 cards. How many bridge deals are possible?

If 12 people are to be divided into 3 committees of respective sizes \(3,4,\) and \(5,\) how many divisions are possible?

If 8 new teachers are to be divided among 4 schools, how many divisions are possible? What if each school must receive 2 teachers?

If 8 identical blackboards are to be divided among 4 schools, how many divisions are possible? How many if each school must receive at least 1 blackboard?

An elevator starts at the basement with 8 people (not including the elevator operator) and discharges them all by the time it reaches the top floor, number \(6 .\) In how many ways could the operator have perceived the people leaving the elevator if all people look alike to him? What if the 8 people consisted of 5 men and 3 women and the operator could tell a man from a woman?