Determine the number of functions f 1 2 3 4 a b c z suc

Determine the number of functions f : {1, 2, 3, 4} {a, b, c, . . . , z},

such that f(1) = f(2), or f(3) = f(4), or f(1) doesnt equal f(3).

Solution

For the value f(1) we have 26 distinct values in a..z similiarly for f(2) as well.

So, for f(1)=f(2), we have 26 functions

Similiarly for f(3)=f(4) , we have 26 values

for f(1) not equal to f(3) , we subtract the equal cases from total cases.

equal cases: 26

total cases : 26*26

for f(1) not equal to f(3): 26*26-26 number of functions= 650 functions