Exam 10: Counting Methods

Solve the problem. -A computer printer allows for optional settings with a panel of four on-off switches in a row. How many different settings can be selected if no three adjacent switches can all be off?

A shirt company has 3 designs, each of which can be made with short or long sleeves. There are 7 color patterns available. How many different types of shirts are available from this company?

Solve the problem. -There are 12 members on a board of directors. If they must form a subcommittee of 3 members, how many different subcommittees are possible?

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

Solve the problem. -A musician plans to perform 5 selections for a concert. If he can choose from 7 different selections, how many ways can he arrange his program?

Evaluate the expression. - ${ } _ { 6 } \mathrm { C } _ { 0 }$

Solve the problem. -At a lumber company, shelves are sold in 4 types of wood, 2 different widths and 5 different lengths. How many different types of shelves could be ordered?

If two fair dice, one red and one white, are rolled, in how many ways can the result be obtained? -The sum of the numbers showing is either 4 or 5 and the white die is a 2.

Solve the problem. -Find the number of different subsets of the set {9, 10, 11}.

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

A poker hand consists of 5 cards dealt from an ordinary deck of 52 playing cards. How many different hands are there consisting of four hearts and one spade?

Provide an appropriate response. -Consider the following counting problem. How many different sequences of 3 letters can be formed using the letters a, b, c, d, e if repetition is allowed? To solve this problem which of the following rules would you use?

Of the 2,598,960 different five-card hands possible from a deck of 52 playing cards, how many would contain no face cards?

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. -Rotate 180° counterclockwise 6 7 2 1 5 9 8 3 4

If two fair dice, one red and one white, are rolled, in how many ways can the result be obtained? -A 5 is on at least one of the dice.

Solve the problem. -Find the number of different subsets of the set {mom, dad, son, daughter}.

Provide an appropriate response. -Consider the arrangements of the letters in the word ALGEBRA. Is this a combination, a permutation, or neither?

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. -Greater than 10

Evaluate the factorial expression. -10!

Solve the problem. -How many three-digit numbers have the sum of their digits equal to 20?