Question

Find the number of ways of arranging $m$ numbers out of $1,2,3,.....,n$ so that maximum is $(n-2)$ and minimum is $2$ (repetitions of numbers is allowed ) such that maximum and minimum both occur exactly once, $(n>5,m>3)$ is

• A. ${}^{n-3}{C}_{m-2}$
• B. ${}^m{C}_2(n-3{)}^{m-2}$
• C. $m(m-1)(n-5{)}^{m-2}$
• D. ${}^n{C}_2{\cdot }^n{C}_m$

Answer 1

The correct option is A ${}^{n-3}{C}_{m-2}$

From the total number of numbers $1\to n$ Only $n-3$ can be selected because $1,n-1,n$ cannot be included ,.So the no .of ways are ${}^{n-3}{C}_m$