A group of health care providers consists of 4 doctors, 3 dentists, and 5 nurses. How many combinations of 2 health care providers of different types are possible?

The number of combinations of 2 health care providers of different types possible are 47.

Explanation:

Doctors = 4

Dentists = 3

Nurses = 5

combinations of two different health care providers = ?

Combination would be = ⁴C₁ X ³C₁ + ³C₁ X ⁵C₁ + ⁴C₁ X ⁵C₁

ⁿCₐ = n! / (n - a) ! X a!

So on calculating the combination we get,

= 4 X 3 + 3 X 5 + 4 X 5

= 12 + 15 + 20

= 47

Therefore, the number of combinations of 2 health care providers of different types possible are 47.