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 $.
Statement $-1$ is false, Statement $-2$ is true.
Statement $- 1$ is true, Statement $-2$ is false.
Statement$-1$ is true, Statement $-2$ is true; Statement $-2$ is a not correct explanation for Statement $-1$
Statement$-1$ is true, Statement $-2$ is true; Statement $-2$ is a correct explanation for Statement $-1$
A committee of $11$ members is to be formed from $8$ males and $5$ females. If $m$ is the number of ways the committee is formed with at least $6$ males and $n$ is the number of ways the committee is formed with at least $3$ females, then
If $^{10}{C_r}{ = ^{10}}{C_{r + 2}}$, then $^5{C_r}$ equals
A person is permitted to select at least one and at most $n$ coins from a collection of $(2n + 1)$ distinct coins. If the total number of ways in which he can select coins is $255$, then $n$ equals
The least value of a natural number $n$ such that $\left(\frac{n-1}{5}\right)+\left(\frac{n-1}{6}\right) < \left(\frac{n}{7}\right)$, where $\left(\frac{n}{r}\right)=\frac{n !}{(n-r) ! r !}, i$
Six ‘$+$’ and four ‘$-$’ signs are to placed in a straight line so that no two ‘$-$’ signs come together, then the total number of ways are