find the number of surjections from A to B where A={1,2,3,4} and B= {a,b,c} . please explain :)
1357a surjection is an onto function
cases .. a is mapped by 2 elements of A.
b by 1 and c by 1
no of ways = 4C22C21C1
now this can be done in three ways.. in the sense that there could be 2 elements pointing to a or to b ro to c
hence 3. 4C22C21C1
1i think she is right ..if b is mapped by one element then it should be 2C1 but in that case answer would be 36 which is not even in the options Options are 10,18,14,16
66The answer is indeed 36.
In general, if set A has n elements and set B has m elements, where m\leq n, then the number of surjections from A to B is
\sum_{k=0}^m \ (-1)^k\binom{m}{k} (m-k)^n
Here, \binom{m}{k} is the binomial number mCk. For the present case, n=4 and m=3.
62cases .. a is mapped by 2 elements of A.
b by 1 and c by 1
no of ways = 4C22C11C1
now this can be done in three ways.. in the sense that there could be 2 elements pointing to a or to b ro to c
hence 3. 4C22C11C1
= 3.6.2=36
