Four balls are selected at random without replacement from an urn containing three white balls and six blue balls. Find the probability of the given event.
All of the balls are blue.

A)
B)
C)
D)
E) 1
F) 0

Question

Four balls are selected at random without replacement from an urn containing three white balls and six blue balls. Find the probability of the given event. ​
All of the balls are blue.
​
A) ​ 
B) ​ 
C) ​ 
D) ​ 
E) 1 
F) 0

Quizplus · Accepted Answer

The number of ways to choose 4 balls out of the 9 is ${9\choose4}$.
The number of ways to choose 4 blue balls out of the 6 is ${6\choose4}$.
Therefore, the probability of choosing 4 blue balls is ${6\choose4}/{9\choose4}$.
Simplifying this expression gives us (6x5)/(9x8) = 5/12.
Therefore, the answer is choice C.

Four Balls Are Selected at Random Without Replacement from an Urn