A theater group offers souvenir t-shirts in 4 different sizes (Small, Medium, Large, and E… — ACT

A theater group offers souvenir t-shirts in $4$ different sizes (Small, Medium, Large, and Extra-Large) and $5$ different colors. In addition, each t-shirt can be printed either with or without a custom emblem on the front. How many distinct t-shirt design options are available?

A
$11$
B
$20$
$40$ Answer
D
$80$
E
$100$

Answer

There are 40 distinct t-shirt design options available.

According to the Fundamental Counting Principle, to find the total number of distinct outcomes from a series of independent choices, multiply the number of choices available for each feature. Since there are

4

sizes,

5

colors, and

2

emblem choices (with or without an emblem), the total number of distinct t-shirt options is

4 \times 5 \times 2 = 40

Step-by-Step Solution

Identify the number of independent choices for each attribute.

Size choices = 4; Color choices = 5; Emblem choices = 2 (with emblem or without emblem).

Each attribute represents an independent stage of selection.

Apply the Fundamental Counting Principle.

Total options =

4 \times 5 \times 2 = 40

When an event consists of multiple sequential independent choices, the total number of outcomes is the product of the number of options for each choice.

Key Concept

Fundamental Counting Principle

Estimated Time:45s

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