While selecting candy for students In his class, Professor Murphy must choose between gummy candy and llcorice nlbs. Gummy candy packets come In four sizes, while packets of licorice nibs come In three. If he chooses gummy candy, he must select gummy bears, gummy worms, or gummy dinos. If he chooses licorlce nibs, he must choose between red and black. How many cholces does he have? HINT [See Example 2.]

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While selecting candy for students In hls class, Professor Murphy must choose between gummy candy and
licorice nibs. Gummy candy packets come In four sizes, while packets of licorice nibs come In three. If he
chooses gummy candy, he must select gummy bears, gummy worms, or gummy dinos. If he chooses licorlce
nibs, he must choose between red and black. How many cholces does he have? HINT [See Example 2.]
Step 1
Professor Murphy must first choose between gummy candy and licorice nibs. Below we outline a definite
procedure that he can use to decide whlch candy packets to choose.
Alternative 1: Gummy Candy
Step 1: pick a size (they come in 4 sizes)
Step 2: pick a shape (bears, worms, dinos)
Alternative 2: Licorice nibs
Step 1: pick a size (they come in 3 sizes)
Step 2: pick a color (red and black)
That is, he can choose between alternative 1 and alternative 2. If he chooses alternative 1 he has a sequence
of two choices to make: size and shape. If he chooses alternative 2 he has a sequence of two choices to
make: size and color.
Recall the multiplication principle, which states that when making a sequence of choices with r steps, suppose
that step 1 has n, possible outcomes, step 2 has n, possible outcomes, . .., step r has n, possible outcomes
and that each sequence of choices results in a distinct outcome, then there are a total of n, x n x ...Xn,
possible outcomes.
We will first consider alternative 1. Step 1 is to pick a size, for which there are 4 options. Step 2 is to pick a
shape, for which there are
options. Therefore, by the multiplication principle, there are
possible choices for alternative 1.
Now we consider alternative 2. Step 1 is to pick a size, for which there are 3 options. Step 2 is to pick a color,
for which there are
options. Therefore, by the multiplication principle, there are
possible choices for alternative 2.
Transcribed Image Text:While selecting candy for students In hls class, Professor Murphy must choose between gummy candy and licorice nibs. Gummy candy packets come In four sizes, while packets of licorice nibs come In three. If he chooses gummy candy, he must select gummy bears, gummy worms, or gummy dinos. If he chooses licorlce nibs, he must choose between red and black. How many cholces does he have? HINT [See Example 2.] Step 1 Professor Murphy must first choose between gummy candy and licorice nibs. Below we outline a definite procedure that he can use to decide whlch candy packets to choose. Alternative 1: Gummy Candy Step 1: pick a size (they come in 4 sizes) Step 2: pick a shape (bears, worms, dinos) Alternative 2: Licorice nibs Step 1: pick a size (they come in 3 sizes) Step 2: pick a color (red and black) That is, he can choose between alternative 1 and alternative 2. If he chooses alternative 1 he has a sequence of two choices to make: size and shape. If he chooses alternative 2 he has a sequence of two choices to make: size and color. Recall the multiplication principle, which states that when making a sequence of choices with r steps, suppose that step 1 has n, possible outcomes, step 2 has n, possible outcomes, . .., step r has n, possible outcomes and that each sequence of choices results in a distinct outcome, then there are a total of n, x n x ...Xn, possible outcomes. We will first consider alternative 1. Step 1 is to pick a size, for which there are 4 options. Step 2 is to pick a shape, for which there are options. Therefore, by the multiplication principle, there are possible choices for alternative 1. Now we consider alternative 2. Step 1 is to pick a size, for which there are 3 options. Step 2 is to pick a color, for which there are options. Therefore, by the multiplication principle, there are possible choices for alternative 2.
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