In how many ways can you place on a chessboard so that they do not attack each other

a) two rooks; b) two kings; c) two bishops; d) two knights; e) two queens?

All figures are of the same color.
In part a) the answer is half of that in problem 102877, and in part b) - of that in problem 30327, since in those calculations each position was counted twice. In the other parts, the calculations are similar.

## Answer

a) $\frac{64 \cdot 49}{2}=1568 ;$ b) $\frac{4 \cdot 60+24 \cdot 58+36 \cdot 55}{2}=1806$ ways; c)

$\frac{28 \cdot 56+20 \cdot 54+12 \cdot 52+4 \cdot 50}{2}=1736$ ways;

d) $\frac{4 \cdot 61+8 \cdot 60+20 \cdot 59+16 \cdot 57+15 \cdot 55}{2}=1848$ ways; e)

$\frac{28 \cdot 42+20 \cdot 40+12 \cdot 38+4 \cdot 36}{2}=1288$ ways.