- #1
22990atinesh
- 143
- 1
Homework Statement
Consider Sets A={1,2,3,...,n} and B={1,2,3,...,m} where 1<=n<=m. F:A->B
1) Total no. of strictly increasing function i.e if x<y then f(x)<f(y)
2) Total no. of non decreasing function i.e if x<y then f(x)<=f(y)
How can we count total number of functions here
2. The attempt at a solution
1st element in set A has [(m-1)-n+1] choices
2nd ... [(m-2)-n+1] choices
3rd ... [(m-3)-n+1] choices
and so on
So for 1) I'm getting (m-1)(m-2)(m-3)...(m-2n+1)
Is it the correct approach