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.
3. A combination is an ordered arrangement of objects.

Design Your Own Lottery You have been given the task of creating a new lottery. For each $1 ticket, the player will select 6 different numbers from 1 to 25 (without replacement), and the only prize will be the jackpot won by players who select the six numbers (in any order) that are later drawn.

a. What is the probability of winning with one ticket?

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.

Matching Probabilities In Exercises 11-16, match the event with its probability.

a. 0.95

b. 0.005

c. 0.25

d. 0

e. 0.375

f. 0.5

16. You toss a coin four times. What is the probability of tossing tails exactly half of the time?

1. When you calculate the number of permutations of n distinct objects taken r at a time, what are you counting? Give an example.

In Exercises 7-14, perform the indicated calculation.

9.8C3

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

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

17. The number of ways 2 captains can be chosen from 28 players on a lacrosse team

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?