Five balls are selected at random without replacement from a

Five balls are selected at random without replacement from an urn containing four white balls and six blue balls. Find the probability of the given event. (Round your answer to three decimal places.)

All of the balls are blue

Solution

Total number of blue balls=6

We can pick 5 blue balls in 6C₅ ways

ie, 6C₅=6!/5!1! =6

Total number of balls =10

We can pick any 5 balls in 10C₅ ways

ie, 10C₅=10!/5!5!

             = (5!*6*7*8*9*10) / 5!*5!

             =(6*7*8*9*10) / 5!

             =(6*7*8*9*10) / (1*2*3*4*5)

             =252

Then, the probability of the event if all of the balls are blue , p = 6 / 252

                                                                                                  =0.0238

                                                                                            = appr 0.024