Final answer:
There are 126 ways to choose a group of five to work on the project. Option number C is correct.
Step-by-step explanation:
To determine the number of ways a group of five can be chosen from a team of nine members, we can use the concept of combinations. The formula for combinations is n choose r, where n is the total number of members and r is the number we want to choose. In this case, we want to choose a group of five from a team of nine, so the formula becomes 9 choose 5.
To calculate this, we can use the formula for combinations: C(n, r) = n! / (r!(n-r)!).
Plugging in the values, we have 9! / (5!(9-5)!), which simplifies to (9! / (5! * 4!)).
Calculating the factorial values, we get (9 * 8 * 7 * 6 * 5!) / (5! * 4!), which further simplifies to (9 * 8 * 7 * 6) / (4 * 3 * 2 * 1).
Finally, we can cancel out common factors and calculate the value: (9 * 8 * 7 * 6) / (4 * 3 * 2 * 1) = 9 * 2 * 7 = 126.
Therefore, there are 126 ways to choose a group of five to work on the project.