A Finite student has a set of differently shaped plastic objects. There are 3 pyramids, 4
cubes, and 7 spheres.
a) In how ways can the objects be arranged in a row if each is a different color?
b) How many arrangements are possible if objects of the same shape must be grouped
together and each object is a different color?
c) In how many distinguishable ways can the objects be arranged in a row if objects of the
same shape are also the same color but need not be grouped together?
d) In how many ways can you select 3 objects, one of each shape, if the order in which the
objects are selected does not matter and each object is a different color?
e) In how many ways can you select 3 objects, one of each shape, if the order in which the
objects are selected matters and each object is a different color?
#2: (Section 8.1)
The game of Sets uses a special deck of cards. Each card has either one, two, or three
identical shapes, all of the same color and style. There are three possible shapes: squiggle,
diamond, and oval. There are three possible colors: green, purple, and red. There are three
possible styles: solid, shaded, or outline. The deck consists of all possible combinations of
shape, color, style, and number of shapes. How many cards are in the deck?
#3: (Section 8.2)
The coach for the Finite Baseball team has 5 good hitters and 4 poor hitters on the bench. He
chooses 3 players at random for the line-up. In how many ways can he choose at least 2 good
hitters?
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