4. Probability

31. Experiment A researcher is randomly selecting a treatment group of 10 human subjects from a group of 20 people taking part in an experiment. In how many different ways can the treatment group be selected?

In Exercises 15-18, determine whether the situation involves permutations, combinations, or neither. Explain your reasoning.

15. The number of ways 16 floats can line up in a row for a parade

Mega Millions As of this writing, the Mega Millions lottery is run in 44 states. Winning the jackpot requires that you select the correct five different numbers from 1 to 70 and, in a separate drawing, you must also select the correct single number from 1 to 25.

c. How does the probability compare to the probability for the old Mega Millions game which involved the selection of five different numbers between 1 and 75 and a separate single number between 1 and 15?

Social Security Numbers A Social Security number consists of nine digits in a particular order, and repetition of digits is allowed. After seeing the last four digits printed on a receipt, if you randomly select the other digits, what is the probability of getting the correct Social Security number of the person who was given the receipt?

Emily is organizing her closet. She has 15 shirts left to hang but has space in one section for 6 shirts. How many ways could she hang shirts in that section?

34. Lottery Number Selection A lottery has 52 numbers. In how many different ways can six of the numbers be selected? (Assume the order of selection is not important.)

In the game of Jumble, the letters of a word are scrambled. The player must form the correct word. In a recent game in a local newspaper, the Jumble “word” was LINCEY. How many different arrangements are there of the letters in this “word”?

Pick 10 Lottery For the New York Pick 10 lottery, the player first selects 10 numbers from 1 to 80. Then there is an official drawing of 20 numbers from 1 to 80. The prize of \$500,000 is won if the 10 numbers selected by the player are all included in the 20 numbers that are drawn. Find the probability of winning that prize.

5. Use technology to randomly select two numbers from 1 to 6. Find the sum and subtract 1 to obtain a total.

a. What is the theoretical probability of each total from 1 to 11?

b. Use this procedure to select 100 totals from 1 to 11. Tally your results and compare them with the probabilities in part (a).

20. Skating Eight people compete in a short track speed skating race. Assuming that there are no ties, in how many different orders can the skaters finish?

Evaluate the given expression. $_{11}C_7$

From a class of 28 students, in how many ways could a teacher select 4 students to lead the class discussion?

List all permutations of five objects a, b, c, d, and e taken three at a time without replacement.

True or False? In Exercises 3-6, determine whether the statement is true or false. If it is false, rewrite it as a true statement.

6. 7C5=7C2

7. There are 16 students giving final presentations in your history course.

b. Presentation subjects are based on the units of the course. Unit B is covered by three students, Unit C is covered by five students, and Units A and D are each covered by four students. How many presentation orders are possible when presentations on

the same unit are indistinguishable from each other?