Question

(+5)* 6. Suppose that a box contains 2 red balls, 3 white balls, and 4 blue balls. Suppose also that balls are selected from the box one at a time, at random, without replacement. What is the probability that a) all white balls will be obtained in a row? b) both end balls are blue?

Answer 1

a)
total number of balls = 2+3+4 = 9
total number of arrangement = 9!/(2!*3! * 4!) = 1260

number of arrangement such that all white balls are in a row
make all white balls as 1 (X)
X, RR,BBBB
hence number of arrangement = 8!/(2! * 4!) = 840

hence required probability = 840/1260
= 2/3

b)
both ends are blue

hence remaing 6 balls RR,BB,WWW
= 7!/(2! *2! * 3!) = 210
required probbaility = 210/1260
= 1/6