In how many different ways can the letters of the word '$BANKING$' be arranged?

Statement-$1$: The number of ways of distributing $10$ identical balls in $4$ distinct boxes such that no box is empty is $^9C_3$.
Statement-$2$: The number of ways of choosing any $3$ places from $9$ different places is $^9C_3$.

The number of $3$-digit odd numbers that can be formed by using the digits $1, 2, 3, 4, 5, 6$ when the repetition is allowed,is

$A$ question paper had ten questions. Each question could only be answered as True $(T)$ or False $(F)$. Each candidate answered all the questions. Yet,no two candidates wrote the answer in an identical sequence. How many different sequences of answers are possible?

There are $3$ girls in a class of $10$ students. The number of different ways in which they can be seated in a row such that no two of the three girls are together is

If ${ }^{2 n} C_{r} = { }^{2 n} C_{r+2}$,find $r$.