CPM Homework Help : CCA2 Problem 12-21

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12-21.

A jar contains five red, four white, and three blue balls. If three balls are randomly selected, find the probability of choosing:

Hint:

Review the Math Notes box in Lesson 10.1.1 to review combinations.

Two red and one white.
Hint (a):
There are $5$ red balls, choose $2$ .
There are $4$ white balls, choose $1$ .
There are $3$ blue balls, choose $0$ .
More Help (a):
There are $12$ balls total, choose $3$ .
Answer (a):
$\frac{_5C_2\;·\;_4C_1·\;_3C_0}{_{12}C_3}=\frac{2}{11}$

Three white.
Hint (b):
See part (a).

One of each color.
Hint (c):
See part (a).
Answer (c):
$\frac{_5C_1\cdot _4C_1\cdot _3C_1}{_{12}C_3}=\frac{3}{11}$

All the same color.
Hint (d):
Find the probabilities of all red balls, all white balls, and all blue balls. Adding these probabilities will give you the total probability that the balls will be all the same color.
Answer (d):
$\frac{_5C_3}{_{12}C_3}+\frac{_4C_3}{_{12}C_3}+\frac{_3C_3}{_{12}C_3}=\frac{3}{44}$

One red and two white.
Hint (e):
See part (a).

Two of one color and one of another.
Hint (f):
Parts (c) and (d) describe the only other color combinations of balls.
Answer (f):
$1-(\frac{3}{11}+\frac{3}{44})\ =\ \frac{29}{44}$

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