Let's draw marbles

Probability Level pending

A box contains 31 white and 27 black marbles. In how many ways can we draw from the box group of 5 balls involving at least 4 white balls?

1 solution

A Former Brilliant Member
Oct 31, 2017

We obtain at least 4 white marbles if we obtain a) Exactly 4 white balls and 1 black ball; or

b) Exactly 5 white balls.

Since a) and b) are mutually exclusive events, we add their numbers of ways of occurrence and obtain the following final result:

$(_{31}C_4)(_{27}C_1)+ _{31}C_5=1019466$