Members of a hospital advisory committee will be selected from 5 doctors and 4 nurses. The committee must have 2 doctors and 2 nurses.
How many possible combinations of doctors and nurses could be chosen for the committee????
7 people
5 Doctors taken 2 at a time
C(5,2) = 5! / [ 2! (5-2)! ] = (5*4* 3) / 3*2 = 10 combinations of doctors
4 nurses, 2 at a time
C(4,2) = 4!/ [ 2! * 2!]= 4*3*2 / 4 = 6
6*10 = 60
To calculate the number of possible combinations, we need to use the concept of combinations. In this problem, we want to choose 2 doctors from 5 and 2 nurses from 4. The formula for combinations is given by:
nCr = n! / r!(n - r)!
Where n is the total number of items, r is the number of items to be selected, and "!" denotes the factorial operation.
For selecting 2 doctors from 5, the calculation would be:
5C2 = 5! / 2!(5-2)!
= (5 * 4 * 3!) / (2 * 1 * 3!)
= (5 * 4) / (2 * 1)
= 10
For selecting 2 nurses from 4, the calculation would be:
4C2 = 4! / 2!(4-2)!
= (4 * 3 * 2!) / (2 * 1 * 2!)
= (4 * 3) / (2 * 1)
= 6
To find the total number of possible combinations, we can multiply the two results:
Total combinations = 10 * 6
= 60
Therefore, there are 60 possible combinations of doctors and nurses that could be chosen for the committee.
To find the number of possible combinations of doctors and nurses that could be chosen for the committee, we can use the concept of combinations.
The number of combinations of selecting k items from a set of n items is given by the formula:
C(n, k) = n! / (k!(n-k)!),
where n! represents the factorial of n, which is the product of all positive integers less than or equal to n.
In this case, we need to select 2 doctors from a group of 5 doctors, and 2 nurses from a group of 4 nurses.
So, the number of possible combinations can be calculated as follows:
C(5, 2) * C(4, 2) = (5! / (2!(5-2)!) * (4! / (2!(4-2)!))
= (5! / (2!3!)) * (4! / (2!2!))
= (5 * 4 * 3!) / (2!3!) * (4 * 3 * 2!) / (2!2!)
= (5 * 4) / 2! * (4 * 3) / 2!
= (20 / 2) * (12 / 2)
= 10 * 6
= 60.
Therefore, there are 60 possible combinations of doctors and nurses that could be chosen for the committee.