Find the number of permutations. How many ways can 12 runners in a race finish first, second, and third?

Do the possible arrangements represent permutations or combinations? Jennifer will invite 3 of her 10 friends to a concert.

Many newspapers carry "Jumble," a puzzle in which the reader must unscramble letters to form words. The letters AGGYB were included in newspapers on the day this exercise was written. How many ways can the letters of AGGYB be arranged? Identify the correct unscrambling, then determine the likelihood of getting that result by randomly selecting one arrangement of the given letters.

There are 5 runners in a race. How many ways are there for the 5 runners to finish first, second, and third place? A. 30 B. 60 C. 120 D. 180

Do the possible arrangements represent permutations or combinations? Jennifer must decide how she and her 3 friends will sit at the concert.

Look for Relationships How is $_{9}\mathrm{C}_{2}$ related to $_{9}\mathrm{C}_{7} ?$ Explain. How can you generalize this observation for any values of $n$ and $r$?

Assume that you roll a standard number cube two times. What is the probability of rolling an even number on the first roll and a number less than 3 on the second roll?

Assume that you roll a standard number cube two times. What is the probability of rolling an even number on the first roll and a number less than $3$ on the second roll?

You have an equally likely chance of choosing any integer from 1 through 50. Find the probability of the given event. A perfect square is chosen.

Do the possible arrangements represent permutations or combinations? Jennifer must decide how she and her 3 friends will sit at the concert.

Solve the matrix equation for the unknown matrix X, or explain why no solution exists.

$$\left. \begin{array} { l l } { A = \left[ \begin{array} { l l } { 4 } & { 6 } \\ { 1 } & { 3 } \end{array} \right] } & { B = \left[ \begin{array} { l l } { 2 } & { 5 } \\ { 3 } & { 7 } \end{array} \right] } \\ { C = \left[ \begin{array} { l l } { 2 } & { 3 } \\ { 1 } & { 0 } \\ { 0 } & { 2 } \end{array} \right] } & { D = \left[ \begin{array} { c c } { 10 } & { 20 } \\ { 30 } & { 20 } \\ { 10 } & { 0 } \end{array} \right] } \end{array} \right.$$

2A = B - 3X

Explain Beth's error. $\frac{_{3} P_{3}}{_{5}{P_{3}}}=\frac{3!}{\frac{5!}{(5-3)!}}=\frac{3 !}{5 ! 2 !}=\frac{1}{40}$

The pickup truck could carry

$$\frac { 1 } { 2 }$$

ton. How many pounds is

$$\frac { 1 } { 2 }$$

ton?

Solve by using the strategy Account for All Possibilities. Mary has $62. She has four more$1 bills than $5 bills. She also has at least one$20 bill. If she holds no other denominations of currency, describe the bills she has.