$A$ bag contains $5$ red marbles,$4$ black marbles,and $3$ white marbles. The number of ways in which $4$ marbles can be drawn so that at most $2$ of them are red is:

If ${}^n C_r$ denotes the number of combinations of $n$ things taken $r$ at a time,then the expression ${}^n C_{r+1} + {}^n C_{r-1} + 2{}^n C_r$ equals

If ${ }^{11} C_4+{ }^{11} C_5+{ }^{12} C_6+{ }^{13} C_7={ }^{14} C_{r}$,then the value of $r$ is

The total number of ways of forming a committee of $5$ members out of $7$ Indians,$6$ Americans,$5$ Russians,and $4$ Australians such that every committee contains at least one member from each country is:

What is the total number of ways of choosing $4$ cards from a pack of $52$ playing cards? In how many of these are the $4$ cards of the same colour?

Statement-$1$: $10$ identical balls can be distributed into $4$ distinct boxes in $^9C_3$ ways such that no box remains empty.
Statement-$2$: Any $3$ positions out of $9$ positions can be selected in $^9C_3$ ways.