The number of maps $f$ from the set $\{ 1,2,3 \}$ into the set $\{ 1,2,3,4,5 \}$ such that $f ( i ) \leq f ( j )$ whenever $i < j$ is (a) 60 (b) 50 (c) 35 (d) 30
(c) Compute the number of maps such that $f ( 3 ) = 5 , f ( 3 ) = 4$ etc. Alternatively, define $g : \{ 1,2,3 \} \rightarrow \{ 1,2 , \ldots , 7 \}$ by $g ( i ) = f ( i ) + ( i - 1 )$. Then, $g$ is a strictly increasing function and its image is a subset of size 3 of $\{ 1,2 , \ldots 7 \}$.
The number of maps $f$ from the set $\{ 1,2,3 \}$ into the set $\{ 1,2,3,4,5 \}$ such that $f ( i ) \leq f ( j )$ whenever $i < j$ is\\
(a) 60\\
(b) 50\\
(c) 35\\
(d) 30