Problem 80 - Algebra and Trigonometry

Question

Write a word problem that can be solved by evaluating \(_{7} C_{3}\)

Step-by-Step Solution

Answer

A word problem that can be evaluated by \(_{7} C_{3}\) is: A school club has 7 members and they need to select a 3-member committee. How many different committees can be formed? There are 35 possible committees.

Step 1: Create the Problem

Create a word problem involving a selection of 3 items from a larger set of 7. Example: A school club has 7 members and they need to select a 3-member committee. How many different committees can be formed?

Step 2: Apply Combination Formula

Apply formula for combination: \(_{n} C_{r} = \frac{n!}{r!(n-r)!}\) where '!' denotes factorial, n is total number of items and r is number of items to select. In this case, n=7 and r=3.

Step 3: Solve the Problem

Plug the numbers into the formula and compute: \(_{7} C_{3} = \frac{7!}{3!(7-3)!} = \frac{7*6*5*4*3*2*1}{(3*2*1)*(4*3*2*1)} = 35. So there are 35 possible committees.