Let A = 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 . Then the number of bijective functions f : A → A such that f ( 1 ) + f ( 2 ) = 3 - f ( 3 ) is equal to

Step-by-step solution

Given the set A = 0 ,   1 ,   2 ,   3 ,   4 ,   5 ,   6 ,   7 . And, also a function f : A → A satisfying f ( 1 ) + f ( 2 ) = 3 - f ( 3 ) ⇒   f ( 1 ) + f ( 2 ) + f ( 3 ) = 3 Since, the range of the function is also A , hence the only possibility satisfying the given condition is: 0 + 1 + 2 = 3 We know that, the number of arrangements of n objects at n places is n ! . Since, the given function is bijective i.e. one-one and onto, hence, the elements 1 ,   2 , &