Exam 10: Counting Methods

Solve the problem. -Find the number of three member committees that could be selected from the group of {Mary, Norman, Paula, Raymond, Sally} given that all club members are eligible to be members of the Committee.

Solve the problem. -A class has 10 boys and 12 girls. In how many ways can a committee of four be selected if the committee can have at most two girls?

Solve the problem. -If a license plate consists of two letters followed by four digits, how many different licenses could be created having at least one letter or digit repeated.

Solve the problem. -Construct a product table showing all possible two-digit numbers using digits from the set {1, 2, 6, 7}. List the even numbers in the table.

Solve the problem. -In how many ways can the letters in the word PAYMENT be arranged if the letters are taken 5 at a time?

Solve the problem. -A sports shop sold tennis rackets in 3 different weights, 3 types of string, and 4 grip sizes. How many different rackets could be sold?

Complete the magic (addition)square. A magic square has the property that the sum of the numbers in any row, column, or diagonal is the same. -Use each number 33, 34, 35, 36, 37, 38, 39, 40, and 41 once. 35 36 37 41 34

Solve the problem. -A musician plans to perform 5 selections for a concert. If he can choose from 9 different selections, how many ways can he arrange his program?

Solve the problem. -How many odd three-digit numbers can be written using digits from the set $\{ 2,3,4,5,6 \}$ if no digit may be used more than once?

Given a magic square, other magic squares may be obtained by rotating, adding, or subtracting a constant value to or from each entry, multiplying each entry by a constant, or dividing each entry by a nonzero constant. Start with the given magic square and perform the indicated operation to find a new magic square. -Subtract 7 9 16 11 14 12 10 13 8 15

How many different three-digit numbers can be written using digits from the set $\{ 1,2,3,4,5 \}$ without any repeating digits?

Solve the problem. -How many five-digit counting numbers contain at least one 6?

Determine the number of figures (of any size)in the design. -Cubes (of any size)

Given a magic square, other magic squares may be obtained by rotating, adding, or subtracting a constant value to or from each entry, multiplying each entry by a constant, or dividing each entry by a nonzero constant. Start with the given magic square and perform the indicated operation to find a new magic square. -Multiply by 4 8 1 6 3 5 7 4 9 2

Solve the problem. -Construct a product table showing all possible two-digit numbers using digits from the set {1, 2, 6, 7}. List the square numbers in the table.

Solve the problem. -A pool of possible jurors consists of 10 men and 16 women. How many different juries consisting of 5 men and 7 women are possible?

Complete the magic (addition)square. A magic square has the property that the sum of the numbers in any row, column, or diagonal is the same. -Use each number 4, 5, 6, 7, 8, 9, 10, 11, and 12 once. 7 6 8 11 4 9

Solve the problem. -Given a group of students: $\mathrm { G } = \{$ Allen, Brenda, Chad, Dorothy, Eric, Frances, Gale $\}$ , count the number of different ways of choosing 4 people for a committee. Assume no one can hold more than one office and that each person is to hold a different position on the committee.

Solve the problem. -Consider all the subsets of {r, s, t, u, v, x}. How many of them have 3 elements?

Solve the problem. -If a given set has thirteen elements, how many of its subsets have somewhere from four through eight elements?