how many ways can a 3 person subcommittee be selected from a committee of 7 people
C(7,3) =
210
To find the number of ways a 3-person subcommittee can be selected from a committee of 7 people, we can use the combination formula, also known as "nCr" formula.
The combination formula can be written as:
nCr = n! / (r!(n-r)!)
Where n represents the total number of people (in this case, 7), and r represents the number of people to be selected (in this case, 3). The exclamation mark (!) denotes the factorial operation.
Substituting the values into the formula:
7C3 = 7! / (3!(7-3)!)
Now, let's calculate each factorial:
7! (7 factorial) = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040
3! (3 factorial) = 3 x 2 x 1 = 6
(7-3)! = 4! (4 factorial) = 4 x 3 x 2 x 1 = 24
Plugging these values back into the formula:
7C3 = 5040 / (6 x 24)
Simplifying the expression:
7C3 = 5040 / 144
The final step is dividing:
7C3 = 35
Therefore, there are 35 different ways to select a 3-person subcommittee from a committee of 7 people.