Question

Let $x_1{x}_2{x}_3{x}_4{x}_5{x}_6$ be a six digit number.The number of such numbers if
$x_1<x_2<x_3<x_4<x_5<x_6$ is

• A. ${}^9{C}_3$
• B. ${}^{10}{C}_3$
• C. ${}^{10}{C}_6$
• D. ${}^9{C}_5$

Answer 1

The correct option is A ${}^9{C}_3$

When $x_1<x_2<x_3<x_4<x_5<x_6$
$($Since we have to form $6$ digit number, $\therefore x_1\ne 0)$
Numbers can be selected in${}^9{C}_6$ ways and can be arrange in $1$ way.
$\therefore$ required ways $={}^9{C}_6={}^9{C}_3$