1.a. Calculate the number of possible lottery tickets if the player must choose 8 numbers from a collection of 42 numbers (1 through 42), where the order does not matter. The winner must match all 8.

b. Calculate the number of lottery tickets if the player must choose 7 numbers from a collection of 64 numbers (1 through 64), where the order does not matter. The winner must match all 7.

c. In which lottery does the player have a better chance of choosing the randomly selected winning numbers?

d. In which lottery does the player have a better chance of choosing the winning numbers if the order in which the numbers appear on the ticket matters?

2.In how many ways can 5 men and 5 women sit in a row if no 2 men sit next to each other?

The number of ways is ____

3.A bag of 10 apples contains 2 rotten apples and 8 good apples. A shopper selects a sample of 4 apples from the bag.

a.How many different samples are possible?

b.How many samples contain all good apples?

c,How many samples contain at least 1 rotten apple?

4.A box contains 16 computer disks, 4 of which are known to have bad sectors. In how many ways can 3 disks be selected, without replacement and without regard to order, so that the following conditions are satisfied?

a.In how many ways can disks be selected so that none have bad sectors?

b.The last problem is to find how many ways that 4 disks may be selected so that there are exactly 2 with no bad sectors.