A box contains coupons labelled 1,2, , 100 . Five coupons are picked at random one after another without replacement. Let the numbers on the coupons be x₁, x₂, , x₅ . What is the probability that x₁>x₂>x₃ and x₃ < x₄ < x₅ ?

Step-by-step solution

100¹⁰ C₅[1 2(3)] ¹⁰⁰ C ₅ 5 ! Suppose 1,2,3,4,5 are = 1 20 Place of 1 is fixed Total arrangements of 5 is 2 and array |l|l|l|l| & & 1 & & 5 array arrangements of 2,3,4 , are . array lllll 2 & 3 & 1 & 4 & 5 4 & 2 & 1 & 3 & 5 4 & 3 & 1 & 2 & 5 array 3way