Exam 10: Counting Methods

Solve the problem. -For a set of 9 elements, find the number of different subsets of size 5.

Solve the problem. -If subsets are formed using only digits from the set {1, 2, 3, 4}, how many subsets can be formed with at least two digits?

Using the 36 possibilities found in the product table for rolling two dice, list and count the outcomes for which the sum (for both dice)is the following. -Multiple of 5

Of the 2,598,960 different five-card hands possible from a deck of 52 playing cards, how many would contain 2 black cards and 3 red cards?

Solve the problem. -Among the 635,013,559,600 possible bridge hands (13 cards each)how many contain at least one card that is not a diamond?

Use a tree diagram showing all possible results when a die is rolled twice. List the ways of getting the following result. -The sum of the numbers showing is either 3 or 4.

Solve the problem. -Suppose that 11 fair coins are tossed. Find the numbers of ways of obtaining exactly 5 heads.

Solve the problem. -Four married couples have reserved eight seats in a row at the theater, starting at an aisle seat. In how many ways can they arrange themselves if the four men occupy the four seats closest to the Aisle?

Solve the problem. -Given a committee of 8 women and 11 men, how many different ways are there to pick a female president, a male treasurer, and a secretary of either gender if one of the men, Pete, says that he Cannot be the treasurer? Assume that none can hold more than one office.

Solve the problem. -If a given set has eight elements, how many of its subsets have at most three elements?

Solve the problem. -Four married couples have reserved eight seats in a row at the theater, starting at an aisle seat. In how many ways can they arrange themselves if no couple is to be separated?

Use a tree diagram showing all possible results when a die is rolled twice. List the ways of getting the following result. -The first die shows a 3.

Using the 36 possibilities found in the product table for rolling two dice, list and count the outcomes for which the sum (for both dice)is the following. -Multiple of 3

Solve the problem. -Suppose there are 8 roads connecting town A to town B and 6 roads connecting town B to town C. In how many ways can a person travel from A to C via B?

Use a tree diagram showing all possible results when four fair coins are tossed. Then list the ways of getting the indicated result. -the same on all four coins

Evaluate the permutation. - ${ } _ { 14 } \mathrm { P } _ { 10 }$

Using the 36 possibilities found in the product table for rolling two dice, list and count the outcomes for which the sum (for both dice)is the following. -Between 7 and 10

Four married couples have reserved eight seats in a row at the theater, starting at an aisle seat. In how many ways can they arrange themselves if no couple is to be separated?

Solve the problem. -If a single card is drawn from a standard 52-card deck, in how many ways could it be a diamond or a face card?

Read each combination value directly from Pascal's Triangle. - ${ } _ { 6 } \mathrm { C } _ { 0 }$