Book edition 6th

Author(s) Sullivan

Pages 1200 pages

ISBN 9780321795465

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Short Answer

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) $1$

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

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 :

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

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

$7 \times 3 \times 3 = 63$ 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 :

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

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

$7 \times 5 = 35$ 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 :

$C (3, 3) = \frac{3!}{3! \times 0!}$

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

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Precalculus Enhanced with Graphing Utilities

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Short Answer

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?

Step by Step Solution

Part 1 Step 1 . Given Information

Part 1 Step 2 . Finding the number of ways

Part 2 Step 1 . Given Information

Part 2 Step 2 . Finding the number of ways

Part 3 Step 1 . Given Information

Part 2 Step 2 . Finding the number of ways

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Precalculus Enhanced with Graphing Utilities

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Short Answer

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?

Step by Step Solution

Part 1 Step 1 . Given Information

Part 1 Step 2 . Finding the number of ways

Part 2 Step 1 . Given Information

Part 2 Step 2 . Finding the number of ways

Part 3 Step 1 . Given Information

Part 2 Step 2 . Finding the number of ways

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Pure Maths

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?