Explanation Given, C ( n , r ) = C ( n , n − r ) → ( 1 ) Let C ( n , n − r ) By the combination formula, C ( n , n − r ) = n ! ( n − r ) ! ( n − ( n − r ) ) ! C ( n , n − r ) = n ! ( n − r ) ! ( n − n + r ) ! C ( n , n − r ) = n ! ( n − r ) ! ( r ) ! Since, C ( n , r ) = n ! r ! ( n − r ) ! Thus, C ( n , n − r ) = C ( n , r ) which is true. Now, prove the above equation (Statement) by the numerical examples. Assume the values of n = 10 and r = 4

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ISBN: 9780134462356

Author: Pirnot

Publisher: PEARSON

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Chapter 12.3, Problem 73E

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C(n, r)=C(n, n−r)

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Chapter 12.3, Problem 72E

Chapter 12.3, Problem 74E

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C ( n , r ) = C ( n , n − r )

Solution Summary: The author explains the statement "C(n,n-r)" by the combination formula.

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Chapter 12 Solutions

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C(n, r)=C(n, n−r)