Problem 65 - Algebra and Trigonometry Real Mathematics, Real People

Question

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

Step-by-Step Solution

Answer

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

Step 1: 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.

Step 2: 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, \( C(40, 12) = \frac{40!}{12!(40-12)!} \).

Step 3: Compute factorial and solve

Next, compute the factorials and simplify the expression. Note that 40! = 40 × 39 × 38 × ... × 3 × 2 × 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.