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

The number of different $5$-digit numbers greater than $50000$ that can be formed using the digits $0, 1, 2, 3, 4, 5, 6, 7$,such that the sum of their first and last digits is not more than $8$,is:

The number of $4$-letter permutations formed using the English alphabet such that the number of distinct vowels is equal to the number of distinct consonants,when repetition is allowed,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 $4$.

The number of permutations of all the letters $AAAABBBC$ in which all the $A$'s appear together in a block of $4$ letters or all the $B$'s appear together in a block of $3$ letters,is-

The number of ways of selecting $15$ teams from $15$ men and $15$ women,such that each team consists of one man and one woman,is