$^{14}C_4 + \sum_{j=1}^{4} {^{18-j}C_3}$ is equal to

If ${}^{n-1}C_3 + {}^{n-1}C_4 > {}^{n}C_3$,then $n$ is just greater than which integer?

All the five-digit numbers in which each successive digit exceeds its predecessor are arranged in increasing order of their magnitude. The $97^{th}$ number in the list does not contain the digit:

In how many ways can a committee of $6$ members be formed from $8$ men and $4$ women such that the committee contains at least $3$ women?

The total number of ways of selecting $4$ letters from all the letters of the word $TSEAMCET$ is

In how many ways can $35$ apples be distributed among $3$ boys such that each boy can have any number of apples?