The number of strictly increasing functions f from the set 1,2,3,4,5,6 to the set 1,2,3, .…

Question

The number of strictly increasing functions $f$ from the set $\{1,2,3,4,5,6\}$ to the set $\{1,2,3, \ldots ., 9\}$ such that $f(i) 
eq i$ for $1 \leq i \leq 6$, is equal to :

Accepted Answer

Case (i) If $f(1)=2$ then ${}^{7}{C}_{5}$ functions

Case (ii) $f(1)=3$ then ${}^{6}{C}_{5}$

Case (iii) $f(1)=4$ then ${}^{5}{C}_{5}$

$\Rightarrow 21+6+1=28$

Solutions · 1