Question

in a certain health center there are 3 doctors, 8 nurses and 2 physicians. in how many ways one can form a group of 5 members consisting of 1 doctor, 3 nurse and 1 physician.

Answer 1

The number of ways to form a group of 5 members consisting of 1 doctor, 3 nurses, and 1 physician can be calculated as follows:

Number of ways to select 1 doctor from 3 = 3C1 = 3

Number of ways to select 3 nurses from 8 = 8C3 = (8*7*6)/(3*2*1) = 56

Number of ways to select 1 physician from 2 = 2C1 = 2

Total number of ways to form the group = number of ways to select 1 doctor * number of ways to select 3 nurses * number of ways to select 1 physician
= 3 * 56 * 2
= 336

Therefore, there are 336 ways to form a group of 5 members consisting of 1 doctor, 3 nurses, and 1 physician from a health center that has 3 doctors, 8 nurses, and 2 physicians.