If $\frac{{}^{n + 2}C_6}{{}^{n - 2}P_2} = 11$,then $n$ satisfies the equation

The sum of all the $4$-digit numbers formed by taking all the digits from ${0, 3, 6, 9}$ without repetition is

If ${}^n P_r = 30240$ and ${}^n C_r = 252$,then the ordered pair $(n, r)$ is equal to

Four-digit numbers with all digits distinct are formed using the digits $1, 2, 3, 4, 5, 6, 7$ in all possible ways. If $p$ is the total number of numbers thus formed and $q$ is the number of numbers greater than $3400$ among them,then $p: q=$

$A$ linguistic club consists of $6$ girls and $4$ boys. $A$ team of $4$ members is to be selected from this group including the selection of a leader (from among these $4$ members) for the team. If the team has to include at most one boy,the number of ways of selecting the team is

Statement-$1$: The number of $4$-digit numbers that can be formed using the digits $1, 2, 3, 4, 5, 6, 7$ which are divisible by $4$ is $200$.
Statement-$2$: $A$ number is divisible by $4$ if its unit digit is divisible by $4$.