Question

Three horses $H_1,H_2,H_3$ enter a field which has 7 portions marked $P_1,P_2,P_3,P_4,P5,P_{6}and{P}_7.$ If no 2 horses are allowed to enter the same portion of the field, in how many ways can the horses graze the grass of the field?

• A. 195
• B. 205
• C. 185
• D. 210
• E. None of these

Answer 1

The correct option is D 210

$H_1$ can graze the grass of either $P_1,or{P}_2.or{P}_3,...,$ or $P_7,$.. that is, in 7 ways. After $H_1$ enters the field, there are 6 portions left for $H_2$, as no 2 horses can enter into the same portion of the field. After first 2 enter the field. $H_3$, can enter the field in 5 ways. $\therefore$ By the fundamental principle or counting, the 3 horses can graze the grass of the field in $7\times 6\times 5=210$ ways.