Question

If set $A=\left\{\right(r,s)|r,s\in W\}$, then the number of element(s) in set $A$ such that ${}^5{C}_r\cdot {}^6{C}_s=1$ is

• A. $0$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is D $4$

Given : ${}^5{C}_r\cdot {}^6{C}_s=1$
We know, ${}^n{C}_r\in N$
$\Rightarrow$ Solution is possible only if ${}^5{C}_r={}^6{C}_s=1$
$\Rightarrow {}^5{C}_r=1$ and ${}^6{C}_s=1$
$\Rightarrow r=0,5$ and $s=0,6$

$\therefore$ Possible pairs $(0,0),(0,6),(5,0),(5,6)$
$\Rightarrow$ Number of elements in set $A=4$