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Just before each Supreme Court session, each of the nine justices shakes hands with every other justice. How many handshakes take place? (IMAGE CAN'T COPY)

A pizzeria offers 11 different toppings. Find the number of different kinds of pizza they could make using a. Three toppings b. Five toppings c. Three toppings or five toppings d. All 11 toppings

Four girls and four boys sit around a merry-go-round.a. In how many different ways can they be arranged with respect to each other so that boys and girls alternate? b. If they seat themselves at random, what is the probability that boys and girls will alternate?

A standard deck of playing cards has 52 cards. a. How many different 5 -card poker hands could be formed from a standard deck? b. How many different 13 -card bridge hands could be formed? c. How can you tell that numbers of combinations are being asked for, not numbers of permutations?

A set has ten elements. Find the number of subsets that contain exactly a. Two elements b. Five elements c. Eight elements (Explain the relationship between this answer and the answer to part a.

A set has five elements, (Elements Can't Copy) a. Find the number of different subsets that contain i. One element ii. Two elements iii. Three elements iv. Four elements v. All five elements vi. No elements b. How many subsets are there altogether? What relationship does this number have to the number of elements in the set? c. Based on your answer to part b, how many subsets would a 10 -element set have? A 100 -element set?

A standard 52 -card deck of playing cards has 4 suits, with 13 cards in each suit. In a particular game, each of the four players is dealt 13 cards at random. a. Find the probability that such a 13 -card hand has i. Exactly five spades ii. Exactly three clubs iii. Exactly five spades and three clubs iv. Exactly five spades, three clubs, and two diamonds b. Which is more probable, getting 4 aces or getting 13 cards of the same suit? Give numbers to support your answer.