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Q. 53

Expert-verified
Found in: Page 856

### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465

# 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?

(a) $63$ (b) $35$ (c) $1$

See the step by step solution

## Part 1 Step 1 . Given Information

We are given an urn containing 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 if 2 balls are white and 1 is red

## Part 1 Step 2 . Finding the number of ways

We know that we have a total of 7 white ball and 3 red balls.The ways to draw 2 white ball and 1 red ball is :

$C\left(7,2\right)×C\left(3,1\right)=\frac{7!}{2!5!}×\frac{3!}{1!2!}$

$\frac{7×6×5!}{2×1×5!}×\frac{3×2!}{1×2!}=\frac{7×6}{2}×\frac{3}{1}$

$7×3×3=63$ ways

## Part 2 Step 1 . Given Information

We are given an urn containing 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 if all 3 balls are white?

## Part 2 Step 2 . Finding the number of ways

We know that we have a total of 7 white ball and 3 red balls.The ways to draw 3 white balls :

$C\left(7,3\right)=\frac{7!}{3!}$

$\frac{7×6×5×4!}{4!×3×2×1}=\frac{7×6×5}{3×2×1}$

$7×5=35$ ways

## Part 3 Step 1 . Given Information

We are given an urn containing 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 if all 3 balls are red?

## Part 2 Step 2 . Finding the number of ways

We know that we have a total of 7 white ball and 3 red balls.The ways to draw 3 red balls :

$C\left(3,3\right)=\frac{3!}{3!×0!}$

$\frac{3!}{3!}=1$ way