Exam 10: Counting Methods

Solve the problem. -Mark can remember only the first 4 digits of his friend's phone number. He also knows that the number has 7 digits and that the last digit is not a 0. If Mark were to dial all of the possible numbers And if it takes him 21 seconds to try each one, how long would it take to try every possibility?

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

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

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

Evaluate the permutation. - ${ } _ { 5 } \mathrm { P } _ { 5 }$

Solve the problem. -How many three-digit counting numbers are even?

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

In how many ways could a group of fourteen people be divided into four groups containing respectively two, three, four, and five people?

Solve the problem. -A restaurant offers salads with 2 types of lettuce, 5 different toppings, and 5 different dressings. How many different salads could be ordered?

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

Provide an appropriate response. -Consider the following counting problem. A pool of possible jurors consists of 11 men and 13 women. How many different juries consisting of 5 women and 7 men are possible? To solve this problem, which of the following rules would you use?

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

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 there are no restrictions on the seating Arrangement?

Provide an appropriate response. -Consider determining how many possible phone numbers are within a particular area code (repeated numbers allowed). Is this a combination, a permutation, or neither?

Solve the problem. -Find the number of different subsets of the set {math, English, history, science, art}.

Solve the problem. -How many three-digit counting numbers do not contain any of the digits 1, 5, 7, 8, or 9?

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

With chosen values for a, b, and c, an oder 3 magic square can be constructed by substituting these values in the generalized form shown here. -Use the given values of a, b, and c to construct an order 3 magic square and give the magic sum. a = 17, b = 3, c = -7

Find the number of ways to get the following card combinations from a 52-card deck. -All diamonds in a five-card hand

Solve the problem. -The chorus has six sopranos and eight baritones. In how many ways can the director choose a quartet that contains at least one soprano?