Permutations
Liberal Arts Mathematics
Answer the following problems from Section 7.2 of the textbook: 1 – 2, 9 – 12, 19 – 22.
For reference, the text of the problems are duplicated below.
For the following exercises, give a whole number that's equal to the given expression.
1. \(3!\)
2. \(9!\)
9. \({}_{4}P_{3}\)
10. \({}_{7}P_{5}\)
11. \({}_{12}P_{10}\)
12. \({}_{14}P_{10}\)
The following exercises involve a horse race with 13 entrants.
19 . How many possible complete orders of finish are there?
20 . An exacta bet is one where the player tries to predict the top two finishers in order. How many possible exacta bets are there for this race?
21 . A trifecta bet is one where the player tries to predict the top three finishers in order. How many possible trifecta bets are there for this race?
22 . A superfecta bet is one where the player tries to predict the top four finishers in order. How many possible superfecta bets are there for this race?
1. 6
2. 362,880
9. 24
10. 2520
11. 239,500,800
12. 3,632,428,800
19. 6,227,020,800
20. 156
21. 1716
22. 17,160
#1 should be 6 ( 3*2*1 )
#2 should be 362,880 ( 9*8*7*6*5*4*3*2*1 )
#9 should be 24 ( 4*3*2 )
#10 should be 2520 ( 7*6*5*4*3 )
#11 should be 239,500,800 ( 12*11*10*9*8*7*6*5*4*3 )
#12 should be 3,632,428,800 ( 14*13*12*11*10*9*8*7*6*5 )
#19 should be 6,227,020,800 (13! = 13*12*11*10*9*8*7*6*5*4*3*2*1 )
#20 should be 156 ( 13_P_2 = 13 * 12 )
#21 should be 1716 ( 13_P_3 = 13*12*11 )
#22 should be 17,160 ( 13_P_10 = 13*12*11*10 )