10 different toys are to be distributed among 10 children. Total number of ways of distributing these toys, so that exactly two children do not get any toy, is

Step-by-step solution

There may be two cases. Case I. Two children get none and one get three and others get one each. Then, total number. of ways = 10! 2! 3! 7! 10! Case II. Two get none and two get 2 each and the others get one each. Then, total number of ways = 10! (2!)^4 6! 10! Hence, total number of ways = (10!)^2 2! 3! 7! + (10!)^2 (2!)^4 6! = (10!)^2 25 (2!)^2 6! 84