Question

A man has 3 fifty rupee notes, 4 hundred rupees notes and 6 five hundred rupees notes in his pocket. If 2 notes are taken at random, what are the odds in favour of both notes being of hundred rupee denomination? 

(a) 1 : 12

(b) 12 : 1 

(c) 13 : 1 

(d) 1 : 13

Answer 1

(a) 1 : 12

Rs 50	Rs 100	Rs 500
3	4	6

Selecting 2 (100 Rs) notes from 4 can be done in 4C₂ = (4 x 3)/(2 x 1) = 6 ways

Selecting 2 from (3 + 4 + 6) = 13 notes can be done in 13C

 = (13 x 12)/(2 x 1) = 78 ways

The odds in favour done of P is P : 1 – P

(i.e.,) = 1/13 : 12/13 = 1 : 12