A small acting club has
6
members. Three of the members are to be chosen for a trip to see a Broadway play. How many different
3
-member groups are possible?
1,2,3,4,5,6.
(1). 1,2,3.
(2). 2,3,4.
(3). 3,4,5.
(4). 4,5,6.
(5). 5,6,1.
(6). 6,1,2.
(7). 1,3.5.
(8). 2,4,6.
(9). 3,5,1.
(10). 4,6,2.
(11). 5,1,3.
(12). 6,2,4.
0
A small acting club has
members. Three of the members are to be chosen for a trip to see a Broadway play. How many different
-member groups are possible?
To find the number of different 3-member groups possible from a small acting club with 6 members, you can use the combination formula.
The combination formula is given by:
C(n, r) = n! / (r!(n-r)!)
Where:
- n is the total number of members in the club (6 in this case)
- r is the number of members to be chosen for the trip (3 in this case)
- n! represents the factorial of n (n factorial)
Plugging in the values into the formula:
C(6, 3) = 6! / (3!(6-3)!)
Simplifying it further:
C(6, 3) = 6! / (3! * 3!)
The factorial of a number is the product of all positive integers less than or equal to that number.
Calculating the factorials:
6! = 6 * 5 * 4 * 3 * 2 * 1 = 720
3! = 3 * 2 * 1 = 6
Now, substituting the factorials into the formula:
C(6, 3) = 720 / (6 * 6)
Cancelling out the common factor:
C(6, 3) = 720 / 36
Simplifying the division:
C(6, 3) = 20
Therefore, there are 20 different 3-member groups possible from the small acting club.