Question

Q No. 01: Frequently doctors experiment with combinations of new drugs to
combat hard to treat illness such as Aids and Hepatitis. Assume that
a pharmaceutical company has developed 5 antibiotics and 4
immune system stimulators. In how many ways can we choose a
treatment program consisting of 3 antibiotics and 2 immune system
stimulators to treat a disease? Use Pascals Triangle to speed up
your computation

Answer 1

Here order is not important so we can use combination formula.

Total ways of chosen 3 antibiotics out of 5 antibiotics = ⁵C₂ = 5!/{(5-3)!*3! }= 5*4/2 = 10 ways

Total ways of chosen 2 immune system stimulators out of 4 stimulators = ⁴C₂ = 4!/{(4-2)!*2! }= 4*3/2 = 6 ways

So total possible ways we can choose a treatment program consisting of 3 antibiotics and 2 immune system stimulators to treat a disease = 10*6 = 60 ways

So answer is 60.