Solve each problem. Show work.
1 From a group of 11 racers, how many top 3 finishes are possible?
2 In how many ways can a subcommittee of 4 be chosen from a senate committee of 6 Democrats and 8 Republicans if...
a. All members are eligible?
b. The subcommittee must consist of 3 Democrats and 1 Republican?
3 How many ways can 3 married couples sit in a row of 6 chairs if...
a. they can sit in any order?
b. the men must sit next to each other and the women must sit next to each other?
4 How many different 6-letter code words can be formed from the first 8 letters of the alphabet if adjacent letters must be different?
5 Two dice are rolled, what is the probability that the sum is 8 OR doubles were rolled?
6 3 cards are drawn from a 52-card deck, what is the probability of getting 2 aces?
7 A shipment of 45 parts, including 9 that are defective, is sent to a plant. The quality control selects 10 at random for testing and rejects the entire shipment if one or more in the sample are defective. What is the probability that the shipment will be rejected?
8 In a group of 15 people, what is the probability that at least 2 of them have the same birthday?
9 A company advertised its products in 2 magazines: Good Housekeeping and Ladies Home Journal. 500 customers revealed that 140 learned of its products from GH, 130 learned of its products from LHJ, and 80 learned of its products from both magazines. What is the probability that a person selected at random from this group saw the company's advertisement in
a. both magazines
b. at least one of the magazines
c. exactly one magazine
10 . A combination lock has 4 wheels, each labeled with 10 digits from 0 to 9. If an opening combination is a particular sequence of 4 digits with no repeats, what is the probability of the person guessing the right combination?