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A computer programming team has 9 members. How many ways can a group of five be chosen to work on a project?

A) 36 ways
B) 84 ways
C) 126 ways
D) 252 ways
E) 504 ways

1 Answer

1 vote

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.

User RWC
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