/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 1076 Evaluate each of the following s... [FREE SOLUTION] | 91影视

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Chapter 34: Problem 1076

Evaluate each of the following symbols: (a) \(\mathrm{C}(6,3)\) (b) \(\mathrm{C}(18,16)\)

Short Answer

Expert verified
\(\mathrm{C}(6,3) = 20\) and \(\mathrm{C}(18,16) = 153\).

Step by step solution

01

(Part (a))

We need to evaluate C(6, 3) using the formula: \[\mathrm{C}(6, 3) = \frac{6!}{3!(6-3)!}\] First, let's calculate the factorials: - 6! = 6 脳 5 脳 4 脳 3 脳 2 脳 1 = 720 - 3! = 3 脳 2 脳 1 = 6 - (6-3)! = 3! = 6 Now, substitute the factorials into the formula and calculate the value: \[\mathrm{C}(6, 3) = \frac{720}{6 \times 6} = \frac{720}{36} = 20\] So, \(\mathrm{C}(6,3) = 20\).
02

(Part (b))

We need to evaluate C(18, 16) using the formula: \[\mathrm{C}(18, 16) = \frac{18!}{16!(18-16)!}\] First, let's calculate the factorials: - 18! = 18 脳 17 脳 16 脳 ... 脳 3 脳 2 脳 1 = 6,402,373,705,728,000 - 16! = 16 脳 15 脳 14 脳 ... 脳 3 脳 2 脳 1 = 20,922,789,888,000 - (18-16)! = 2! = 2 脳 1 = 2 Now, substitute the factorials into the formula and calculate the value: \[\mathrm{C}(18, 16) = \frac{6,402,373,705,728,000}{20,922,789,888,000 \times 2} = \frac{6,402,373,705,728,000}{41,845,579,776,000} = 153\] So, \(\mathrm{C}(18,16) = 153\).

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