A pair of students is selected at random from a probability class. The probability that the pair selected will consist of one male and one female student is 10 19 . Find the maximum number of students the class can contain.

Step-by-step solution

Let t = m + w . We are given that 10 19 = mw ^ t C ₂ = 2 mw t ( t -1) ....(1) But mw m + w 2 or 2 mw t (G.M. A.M.) or m w t ^2 4 ....(2) Substituting mw = ( 10 19 ) ( t ( t -1) 2 ) We have ( 5 19 ) t(t-1) t^2 4 aligned & 20 (t^2-t ) 19 t^2 20 t^2-20 t 19 t^2 or t^2 20 t t 20 & t_ =20 aligned Also equality holds if m = w =10 Maximum children in class =20 Ans.