#1 Outside a home, there is a 10-key keypad with letters A,B,C,D,E,F,G,H,I,andJ that can be used to open the garage if the correct ten-letter code is entered. Each key may be used only once. How many codes are possible?

#2 There are 53 runners in a race. How many ways can the runners finish first, second, and third?

#3 At a blood drive, 6 donors with type O+ blood, 5 donors with type A+ blood, and 2 donors with type B+ blood are in line. In how many distinguishable ways can the donors be in line?

#4 How many different 10-letter words (real or imaginary) can be formed from the following letters?

F, H, F, B, W, N, H, H, J, W

#5 A certain lottery has 32 numbers. In how many different ways can 6 of the numbers be selected? (Assume that order of selection is not important.)

#6 An environmental agency is analyzing water samples from 80 lakes for pollution. Five of the lakes have dangerously high levels of dioxin. Six of the lakes are randomly selected from the sample. Using technology, how many ways could one polluted lake and five non-polluted lakes be chosen?

#7 In a certain lottery, you must correctly select 6 numbers (in any order) out of 35 to win. You purchase one lottery ticket. What is the probability that you will win?

#8 A warehouse employs 24 workers on first shift, 19 workers on second shift, and 12 workers on third shift. Eight workers are chosen at random to be interviewed about the work environment. Find the probability of choosing exactly five first-shift workers.