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Five members of a nine-person committee must be chosen to form a subcommittee. How many different subcommittees could be formed?

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Final answer:

To form the subcommittee, we can use the concept of combinations. Choosing 5 members out of 9, the total number of different subcommittees that can be formed is 1512.

Step-by-step explanation:

To determine the number of different subcommittees that can be formed, we need to use the concept of combinations. In this case, we need to choose 5 members out of 9 to form the subcommittee.



The formula to calculate the number of combinations is:



C(n, r) = n! / (r!(n-r)!)



Where n is the total number of members (9) and r is the number of members chosen (5).



Plugging in the values into the formula:



C(9, 5) = 9! / (5!(9-5)!)



Simplifying the expression:



C(9, 5) = (9 * 8 * 7 * 6 * 5!) / (5! * 4 * 3 * 2 * 1)



Cancelling out the common factors:



C(9, 5) = (9 * 8 * 7 * 6) / (4 * 3 * 2 * 1)



C(9, 5) = 1512



Therefore, there are 1512 different subcommittees that could be formed.

User Matthew Pigram
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