i would like a clear explanation of this problem

Question

A box contains 6 red marbles and 8 blue marbles. If you randomly grab 5 marbles at a time, find
the probability that there will be
(i) 3 red. (ii) 4 red. (iii) all red. (iv) none red (v) none blue

Answer 1

(i) P(3 red) = 6C3•8C2 / 14C5

There are several ways to choose 3 red, from 6 available; others would be 2 red, from 8 available; this product is divided by # ways to choose any five, from the available 14 reds & blues.

 

(ii) P(4 red) = 6C4•8C1 / 14C5 

 

(v)P(all 5 red) = 6C5 / 14C5