An urn contains 5 red, 3 black and 2 white balls. If three balls are chosen at random then what is the probability that balls will be of different colours?
To get 3 balls of different colours, we need to choose 1 ball of each of the three given colours.
So, probability to get 3 balls of different colours =Choosing 1 red, 1 black, 1 white ballsChoosing any 3 from all 10 balls=5C1×3C1×2C110C3
=5×3×210!3!(10−3)! Since nC1=n and nCr=n!r!(n−r)!
=5×3×210!3!7!=5×3×2× 3! × 7!10!= 5×3×2×3 ×2 ×7!10×9×8×7!=14