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.

i hope this is what you were looking for.

see attached graph

option c) graph of line going through 1, 4 and 3, 10

step-by-step explanation:

let y equal to margo's coin collection

let x equal to number of years

at the begining x=0, y=1 → point=(x,y)→point=(0,1)

she adds 3 coins per year, then y=1+3x

at x=1, y=1+3(1)=1+3→y=4→point=(x,y)→point=(1,4)

at x=3, y=1+3(3)=1+9→y=10→point=(x,y)→point=(3,10)

the graph of line going through (1, 4) and (3, 10), then the option c is the correct.