Question

Consider all the six digit numbers that can be formed using the digits $1,2,3,4,5$ and $6$, each digit being used exactly once. Each of such six digit numbers have the property that for each digit, not more than two digits smaller than that digit appear to the right of that digit. Find the number of such six digit numbers having the desired property.

Answer 1

$6$ can be only at one of the last three places $3$ possibility

$6$ is $5$ each also come only in one of last $3$ remaining places.

Continuing similarly we get.

Total no. of possibilities are $3^3\times 2=162$