Question

Three horses $H_1,H_2,H_3$ entered a field which has seven portions marked $P_1,P_2,P_3,P_4,P_5,P_{6}and{P}_7$. If no two horses are allowed to enter the same portion of the field, in how many ways can the horses graze the grass of the field?

Answer 1

$H_1$ can graze the grass of either $P_1$ or $P_2$ or $P_3$... or $P_7$ that is, in $7$ ways.

After $H_1$ entered the field, there are six portions left for $H_2$ as no two can enter into the same portions left for $H_2$ as no two can enter into the same portion of the field.

After first two entered the field $H_3$ can enter the field in $5$ ways.
Therefore, by the fundamental principle of counting, the three horses can graze the grass of the field in
$7\times 6\times 5=210$ ways