Question

A bag contains tickets numbered from 1 to 100. Ten tickets are drawn at random and arranged in ascending order. The number of ways so that fourth and sixth numbers bear 50 and 60 respectively is :

Answer 1

Answer:

Five tickets out of 50 can drawn in 50C5 ways. Since x1 < x2 < x3 < x4 < x5 and x3 = 30, x1 ,x2 < 30, i.e. x1 and x2 should come from tickets numbered 1 and 29 and this may happen in 29C2 ways. Remaining ways, i.e. x4 , x5 > 30, should come from 20 tickets numbered 31 to 50 in 20C2 ways. So, favourable number of cases = 29C2 20C2