Explanation Definition: The combination formula of r elements of a finite set S of n elements is defined as, ( n r ) = n ! r ! ( n − r ) ! For any counting number n , the factorial of n is defined as, n ! = n ( n − 1 ) ( n − 2 ) ....3 ⋅ 2 ⋅ 1 Calculation: Consider a jar which contains four red and six white balls. Three balls are drawn at random. The number of ways of drawing at least one red ball is required. If at least one red ball has to be drawn, it can be one red ball, two red ball and three red balls. So, the possible cases to draw at least one red ball are: Case Red White Number of ways 1 1 2 ( 4 1 ) × ( 6 2 ) 2 2 1 ( 4 2 ) × ( 6 1 ) 3 3 0 ( 4 3 ) × ( 6 0 ) Hence, the number of ways of drawing three balls which has at least one red ball is ( 4 1 ) × ( 6 2 ) + ( 4 2 ) × ( 6 1 ) + ( 4 3 ) × ( 6 0 ) . Use the combination formula and simplify. So,

Nature of Mathematics (MindTap Course List)

13th Edition

ISBN: 9781133947257

Author: karl J. smith

Publisher: Cengage Learning

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Chapter 12.CR, Problem 14CR

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The number of ways to draw at least one red ball from a jar which contains four red and six white balls from which three balls are drawn at random.

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Nature of Mathematics (MindTap Course List)

Ch. 12.1 - IN YOUR OWN WORDS What is a permutation? What is...Ch. 12.1 - Prob. 2PS Ch. 12.1 - Prob. 3PS Ch. 12.1 - Prob. 4PS Ch. 12.1 - Evaluate each expression in Problems 3-32. 9P2 Ch. 12.1 - Evaluate each expression in Problems 3-32. 9P3 Ch. 12.1 - Evaluate each expression in Problems 3-32. 9P4 Ch. 12.1 - Prob. 8PS Ch. 12.1 - Evaluate each expression in Problems 3-32. 52P3 Ch. 12.1 - Evaluate each expression in Problems 3-32. 4P4

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The number of ways to draw at least one red ball from a jar which contains four red and six white balls from which three balls are drawn at random.

Solution Summary: The author calculates the number of ways of drawing at least one red ball from a jar of four red and six white balls when three balls drawn at random are 100.

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To find: The number of ways to draw at least one red ball from a jar which contains four red and six white balls from which three balls are drawn at random.

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Chapter 12 Solutions

To find:

The number of ways to draw at least one red ball from a jar which contains four red and six white balls from which three balls are drawn at random.