ACT Purple Math Lesson 2B: Permutations and Combinations HW HOMEWORK EXERCISES (TIME: 10 MINUTES) 21. The menu at the Good Eats Café contains 6 appetizers, 9 entrées, and 4 desserts. If a three course meal consists of one of each of these, how many different three course meals are possible? (A) (B) (C) (D) (E) 19 114 180 192 216 22. The Riverside High School speech and debate club has 15 members; the musical theatre society has 37. There are 8 students who participate in both activities. If all students active in speech and debate and/or musical theatre attended a picnic, how many students would be there? (A) (B) (C) (D) (E) 36 44 48 52 60 23. In how many ways can 12 kids be split into two distinct teams of 6 for a soccer game? (A) (B) (C) (D) (E) 924 332,640 518,400 665,280 853,776 24. Reggie has 8 dress shirts, 3 pairs of dress pants, 6 neckties, and 3 bowties. An outfit for the school semi-formal dance consists of a shirt, pants, and either a necktie or a bowtie. How many such outfits are possible? (A) (B) (C) (D) (E) 78 216 252 288 432 25. How many three-digit numbers contain at least one even digit? (A) (B) (C) (D) (E) 125 300 375 775 900 26. A hat contains ten balls, each labeled with a number from 1 to 10. Three balls are taken from the hat without replacement, and the numbers on the three balls are added. How many distinct sums are possible? (A) (B) (C) (D) (E) 21 22 24 26 27 27. In a certain city, the five members of the city commission are elected, and then they vote internally to select one of themselves as mayor. If there are eight candidates running, how many distinct city commissions (including choice of mayor) are possible? (A) (B) (C) (D) (E) 56 280 600 1344 6720 28. In how many different orders can six friends line up for a photo, given that two of them are a married couple and must stand next to each other? (A) (B) (C) (D) (E) 48 120 240 576 714 29. How many five-card hands are possible in which four of the five cards are hearts and the remaining card is the queen of another suit? (A) (B) (C) (D) (E) 1485 2145 2860 3861 51,480 30. How many distinct committees of two men and three women can be formed if they are to be chosen from a staff of eight men and twelve women? (A) (B) (C) (D) (E) 64 1568 6160 7392 15,504 Version 3.0 Unauthorized copying or reuse of any part of this page is illegal. 55