$$ \text { If }{ }^{\mathrm{n}} C_{13},{ }^{\mathrm{n}} C_{14} \text { and }{ }^{\mathrm{n}} C_{15} \text { are in arithmetic progression, then the positive integer value of ' } \mathbf{n} \text { ' can be } $$

In how many ways can the squares of a $\mathbf{4} \times \mathbf{2}$ grid ( 4 rows and 2 columns) be filled with the letters of the word 'SPHERE' such that each row contains at least one letter?

A batch of $\mathbf{1 0}$ cupcakes consists of $\mathbf{5}$ chocolate, $\mathbf{3}$ vanilla, and $\mathbf{2}$ strawberry. If 4 cupcakes are selected to be put into a gift box, find the number of different ways they can be chosen if the selection must include at least $\mathbf{2}$ chocolate, at most $\mathbf{1}$ vanilla, and exactly $\mathbf{1}$ strawberry cupcake.

The range of the function $f(x)={ }^{(7-x)} P_{(x-3)}$ is