# mP02B (HW) Permutations and Combinations

```ACT Purple Math
Lesson 2B: Permutations and Combinations
HW
HOMEWORK EXERCISES (TIME: 10 MINUTES)
21. The menu at the Good Eats Caf&eacute; contains 6
appetizers, 9 entr&eacute;es, 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
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