A jewelry maker chooses three beads at random from a bag with 10 beads labeled A, B, C, D, E. F, G, H, I. and J. a. How can you use permutations or combinations to find P(selected beads spell the initials DEB)? What is the probability? b. How can you use permutations or combinations to find P(selected beads are all vowels)? What is the probability?

Find the number of combinations. In how many ways can 11 contestants for an award be narrowed down to 3 finalists?

Nabisco is testing 5 chocolate chip cookies, 4 crackers, and 6 reduced-fat cookies. If it plans to market 2 of the chocolate chip cookies, 3 of the crackers, and 2 of the reduced -fat cookies, how many different combinations are possible?

There are 4 comedians and 5 musicians performing in a variety show. The order in which the performers are chosen is random. a. What is the probability that the first 3 performers are comedians? b. What is the probability that the first two performers are a comedian followed by a musician?

Each bead on a bracelet with three beads is either red, white, or blue. Define the relation R between bracelets $(B_1,B_2)$ where $B_1$ and $B_2$ are bracelets, belongs to R if and only if $B_2$ can be obtained from $B_1$ by rotating it or rotating it and then refleciting it. a) Show that R is an equivalence relation. b) What are the equivalence classes of R?

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

What moral lesson do you consider to be one of the story’s main themes? Support your answer with examples from the text.

State if the possible arrangements represent permutations or combinations, then state the number of possible arrangements. A student chooses at random 4 books from a reading list of 11 books.

State if the possible arrangements represent permutations or combinations, then state the number of possible arrangements. Hugo displays his 8 model planes in a single row.

Sage volunteers to read and play with sick children in a hospital. She selects some erasers at random from a bag to use as prizes. There are 8 alien erasers and 10 flying saucer erasers. a. How many groups of 6 erasers can be formed from the 18 erasers? Explain. b. In how many ways can 3 aliens be selected? Explain. c. In how many ways can 3 aliens and 3 flying saucers be selected? Explain. d. What is the probability that 3 aliens and 3 flying saucers will be selected? Explain.

On Wednesdays at Tara's Taquerfa four tacos are the same price as three burritos. Last Wednesday the Lunch Bunch ordered five tacos and six burritos, and their total bill was $8.58 (with no tax or drinks included). Nobody in the Lunch Bunch can remember the cost of one of Tara's tacos. Help them figure it out.

Simplify each expression. Justify each step. 18u-6(9k-7-10u)+4k

There are 6 tiles numbered 1 to 6 in a box. Two tiles are selected at random without replacement to form a 2-digit number. Jeffrey found the probability that the number selected is 16. Explain his error. The number of ways to select 1 and 6 is given by

$$_6C_2 = 15$$

$$P ( 16 ) = \frac { 1 } { _ { 6 } C _ { 2 } } = \frac { 1 } { 15 }$$

State if the possible arrangements represent permutations or combinations, then state the number of possible arrangements. At the end of a season, 10 soccer teams are ranked by the state.