A student has 3 library cards and 8 books of his interest in the library. Out of these 8 books he does not want to borrow Chemistry part 2 unless he can borrow Chemistry part 1 also. In how many ways can he choose the three books to be borrowed?

In how many ways can the word "CHRISTMAS" be arranged so that the letters '$$\mathrm{C}$$' and '$$\mathrm{M}$$' are never adjacent?

If $$\left[{ }^{n+1} C_{r+1}\right]:\left[{ }^n C_r\right]:\left[{ }^{n-1} C_{r-1}\right]=11: 6: 3$$ then $$n r=$$

$$\text { Find }{ }^n C_{21} \text {, if }{ }^n C_{10}={ }^n C_{12}$$