$^nC_r + ^{n-1}C_r + ...... + ^rC_r =$

If $^8C_r = ^8C_{r+2}$,then the value of $^rC_2$ is

The number of integers $x, y, z, w$ satisfying $x+y+z+w=25$ and $x, y, z \geq -1, w \geq 1$ is

If at the end of a certain meeting,everyone had shaken hands with everyone else,and it was found that $45$ handshakes were exchanged,then the number of members present at the meeting is:

In a conference of $8$ persons,if each person shakes hands with every other person exactly once,then the total number of handshakes is:

The solution set of ${ }^5 C_{x-1} > 2 \cdot { }^5 C_x$ is