Chapter 13.2, Problem 53AYU

Selecting Objects An urn contains 7 white balls and 3 red balls. Three balls are selected. In how many ways can the 3 balls be drawn from the total of 10 balls:

(a) If 2 balls are white and 1 is red?

(b) If all 3 balls are white?

(c) If all 3 balls are red?

To determine

To find: In how many ways can the 3 balls be drawn from the total of 10 balls:

a. If 2 balls are white and 1 is red?

Answer to Problem 53AYU

a. 63

Explanation of Solution

Given:

An urn contains 7 white balls and 3 red balls. Three balls are selected from the total of 10 balls.

Formula used:

$C\left(n,r\right)=\frac{n!}{r!\left(n-r\right)!}$

Calculation:

Number of white balls-7.

Number of red balls-3.

Total number of balls-10.

a. Number of ways selecting of 2 white balls and 1 red ball.

$=C\left(7,2\right)*C\left(3,1\right)$

$\frac{7!}{2!5!}*\frac{3!}{2!1!}$

$7*\frac{6}{2}*3$

$21*3$

63

To determine

To find: In how many ways can the 3 balls be drawn from the total of 10 balls:

b. If all 3 balls are white?

Answer to Problem 53AYU

b. 35

Explanation of Solution

Given:

An urn contains 7 white balls and 3 red balls. Three balls are selected from the total of 10 balls.

Formula used:

$C\left(n,r\right)=\frac{n!}{r!\left(n-r\right)!}$

Calculation:

Number of white balls-7.

Number of red balls-3.

Total number of balls-10.

b. Number of ways selecting 3 white balls.

$=C\left(7,3\right)* C\left(3,0\right)$

$=\frac{7!}{3!4!}*\frac{3!}{3!0!}$

$=35*1$

$=35$

To determine

To find: In how many ways can the 3 balls be drawn from the total of 10 balls:

c. If all 3 balls are red?

Answer to Problem 53AYU

c. 1

Explanation of Solution

Given:

An urn contains 7 white balls and 3 red balls. Three balls are selected from the total of 10 balls.

Formula used:

$C\left(n,r\right)=\frac{n!}{r!\left(n-r\right)!}$

Calculation:

Number of white balls-7.

Number of red balls-3.

Total number of balls-10.

c. Number of ways selecting 3 red balls.

$=C\left(7,0\right)*C\left(3,3\right)$

$=\frac{7!}{0!7!}*\frac{3!}{3!0!}$

$=1*1=1$