Use the formula for _nP_r to evaluate each expression. ₈P₅

Use the formula for _nP_r to evaluate each expression. ₁₀P₄

Use the formula for nPr to evaluate each expression. ₆P₆

Use the formula for nPr to evaluate each expression. ₈P₀

Use the formula for nCr to evaluate each expression. ₉C₅

Use the formula for nCr to evaluate each expression. ₁₀C₆

Use the formula for nCr to evaluate each expression. ₁₁C₄

Use the formula for nCr to evaluate each expression. ₇C₇

Use the formula for _nC_r to evaluate each expression. ₄C₄

Use the formula for nCr to evaluate each expression. ₅C₀

Evaluate each expression.

$\frac{{}_7{P}_3}{3!}{-}_7{C}_3$

Evaluate each expression.

$1-\frac{{}_3{P}_2}{{}_4{P}_3}$

Evaluate each expression.

$\frac{{}_7{C}_3}{{}_5{C}_4}-\frac{98!}{96!}$

Evaluate each expression.

$\frac{{}_4{C}_2{\cdot }_6{C}_1}{{}_{18}{C}_3}$

Use the Fundamental Counting Principle to solve Exercises 29–40. The model of the car you are thinking of buying is available in nine different colors and three different styles (hatchback, sedan, or sport). In how many ways can you order the car?

Use the Fundamental Counting Principle to solve Exercises 29–40. An ice cream store sells two drinks (sodas or milk shakes) in four sizes (small, medium, large, or jumbo) and five flavors (vanilla, strawberry, chocolate, coffee, or pistachio). In how many ways can a customer order a drink?

Use the formula for nCr to solve Exercises 49–56. An election ballot asks voters to select three city commissioners from a group of six candidates. In how many ways can this be done?

Use the formula for nCr to solve Exercises 49–56. Of 12 possible books, you plan to take 4 with you on vacation. How many different collections of 4 books can you take?

Use the formula for nCr to solve Exercises 49–56. You volunteer to help drive children at a charity event to the zoo, but you can fit only 8 of the 17 children present in your van. How many different groups of 8 children can you drive?

Use the formula for nCr to solve Exercises 49–56. To win at LOTTO in the state of Florida, one must correctly select 6 numbers from a collection of 53 numbers (1 through 53). The order in which the selection is made does not matter. How many different selections are possible?

How many four-digit odd numbers less than 6000 can be formed using the digits 2, 4, 6, 7, 8, and 9?

Retaining the Concepts. Solve and determine whether 8(x - 3) + 4 = 8x - 21 is an identity, a conditional equation, or an inconsistent equation.

Retaining the Concepts. Expand: ${\log }_7\left(\frac{5\sqrt{x}}{49y^{10}}\right)$

In Exercises 11–16, a die is rolled. Find the probability of getting a 4.

In Exercises 11–16, a die is rolled. Find the probability of getting an odd number.

In Exercises 11–16, a die is rolled. Find the probability of getting a number greater than 4.

You are dealt one card from a standard 52-card deck. Find the probability of being dealt a queen.

In Exercises 17–20, you are dealt one card from a standard 52-card deck. Find the probability of being dealt a picture card.

In Exercises 21–22, a fair coin is tossed two times in succession. The sample space of equally likely outcomes is {HH,HT,TH,TT}. Find the probability of getting two heads.

In Exercises 39–44, you are dealt one card from a 52-card deck. Find the probability that you are not dealt a king.