In how many ways can a committee be formed of $5$ members from $6$ men and $4$ women if the committee has at least one woman?

$A$ die is rolled three times. Find the probability of getting a larger number than the previous number each time.

In a library,there are $n$ distinct books and each has $p$ copies. What is the number of ways to select one or more books?

The domain of definition of the function $f(x) = \log_{[x + \frac{1}{x}]} |x^2 - x - 6| + ^{16-x}C_{2x-1} + ^{20-3x}P_{2x-5}$ is,where $[x]$ denotes the greatest integer function.

From $5$ consonants and $5$ vowels,how many words can be formed using $3$ consonants and $2$ vowels?

If ${ }^9 C_3+{ }^9 C_5={ }^{10} C_r$ for some $r \in N$,then $r=$