Question
Question: There are two bags each of which contains n balls. A man has to select an equal number of balls from...
There are two bags each of which contains n balls. A man has to select an equal number of balls from both the bags. The number of ways in which a man can choose at least one ball from each bag is –
A
2nCn
B
(nCn)2
C
2nC1
D
2nCn – 1
Answer
2nCn – 1
Explanation
Solution
No. of ways of selecting r balls from a bag containing n balls = nCr
\ No. of ways of selecting r balls from each of two bags and each containing balls
= nCr × nCr = (nCr)2.
\ No. of ways of choosing at least one ball from each bag
= (nC1)2 + (nC2)2 + .... + (nCn)2
= [(nC0)2 + (nC1)2 + (nC2)2 + ..... + (nCn)2] – (nC0)2
= 2nCn – 1. [Using (nC0)2 + ...... + (nCn)2 = 2nCn].