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Chapter 9: Problem 65

In how many different ways can a jury of 12 people be randomly selected from a group of 40 people?

Short Answer

Expert verified
The number of different ways a jury of 12 people can be selected from a group of 40 is \( C(40, 12) \)

Step by step solution

01

Identify the values

First, identify the total number of items, or 'n', and the number of items to select, or 'r'. Here, there are 40 people total, making n = 40. We are trying to form a jury of 12 people, so r = 12.
02

Apply the combination formula

Then, apply the combination formulas. Plug the given values of n and r into the combination formula: \( C(n, r) = \frac{n!}{r!(n-r)!} \). So, \( C(40, 12) = \frac{40!}{12!(40-12)!} \).
03

Compute factorial and solve

Next, compute the factorials and simplify the expression. Note that 40! = 40 脳 39 脳 38 脳 ... 脳 3 脳 2 脳 1, and similarly for 12! and 28!. After calculations, the number of ways to select a jury of 12 from 40 people can be found.

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