Eight chairs are numbered 1 to 8. Two women and three men wish to occupy one chair each. First the women choose the chairs from amongst the chairs marked 1 to 4; and then the men select the chairs from amongst the remaining. The number of possible arrangements is

The value of the expression $$\,{}^{47}{C_4} + \sum\limits_{j = 1}^5 {^{52 - j}\,{C_3}} $$ is equal to

The third term of a geometric progression is 4. The product of the first five terms is

If $$x,\,y$$ and $$z$$ are $$pth$$, $$qth$$ and $$rth$$ terms respectively of an A.P. and also of a G.P., then $${x^{y - z}}\,{y^{z - x}}\,{z^{x - y}}$$ is equal to :