Question

The number of functions $f$ from the set $A=\{0,1,2\}$ in to the set $B=\{0,1,2,3,4,5,6,7\}$ such that $f\left(i\right)<f\left(j\right)$ for $i<j$ and $i,j\in A$ is

• A. ${}^8{C}_3$
• B. ${}^8{C}_3+2{(}^8{C}_2)$
• C. ${}^{10}{C}_3$
• D. ${}^{10}{C}_4$

Answer 1

The correct option is A ${}^8{C}_3$

from the given condition we can know that the elements and codomain are not equal and three are distinct

$\because$ selecting three distinct elements in set Band arranging them in assending order will give us the codomain

selecting three elements in set of 8 elements is ${}^8{C}_3$