Fifteen football players of a club-team are given 15 T-shirts with their names written on the backside. If the players pick up the T-shirts randomly, then the probability that at least 3 players pick the correct T-shirt is

Step-by-step solution

Given, Fifteen football players of a club-team are given 15 T-shirts with their names written on the backside So, total sample space will be 15 ! Now for at least 3 players pick the correct T-shirt, Required probability = 1 - D 15 + C 1 15 · D 14 + C 2 15 D 13 15 ! Where D n is de-arrangement and D n ≈ n ! e   where  e ≈ 2 . 73 Taking D 15 as 15  !  e , D ( 14 ) as 14 ! e and D ( 13 ) as 13 ! e We get , 1 - 15 ! e + 15 · 14 ! e + 15 × 14 2 × 13 ! e 15 ! = 1 - 1 e