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

The horses who entered the field : h1 , h2 , h3

Number of horses who entered the field = 3

The given portions into which the horses are made to enter : p1 , p2 , p3 , p4 , p5 , p6 , p7

Total number of portions = 7

So, we need to find the number of ways in which the horses are made to enter the 7 portions given that no two horses can enter the same portion

Now, h1 horse can graze the grass in 7 ways

Also, h2 can graze the grass in 6 ways

And, h3 can graze the grass in 5 ways.

So, Total number of ways = 7 × 6 × 5

Hence, The total number of ways in which the horses can graze the grass of the field = 210