The number of $4$-digit numbers without repetition that can be formed using the digits $1, 2, 3, 4, 5, 6, 7$ in which each number has two odd digits and two even digits is:

If $^nC_r = 84$,$^nC_{r-1} = 36$,and $^nC_{r+1} = 126$,then $n = ..........$

$A$ bag contains $3$ coins of one rupee,$4$ coins of fifty paise,and $5$ coins of ten paise. If at least one coin is selected from the bag,what is the total number of ways to make the selection?

The number of solutions of the equation $x+y+z=10$, where $x, y$, and $z$ are positive integers, is:

The number of ways of selecting a committee of $30$ persons from $20$ boys,$20$ girls,and $20$ teachers such that the participation of the number of boys,girls,and teachers in that committee is equal,is

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 $^9C_3$.