Three horses H1,H2,H3 entered a field which has seven portions marked P1,P2,P3,P4,P5,P6 and P7. 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?

Question

Three horses H1​,H2​,H3​ entered a field which has seven portions marked P1​,P2​,P3​,P4​,P5​,P6​ and P7​. 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?

Filo · Accepted Answer

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

Question Text	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 Type	Text solution:1
Upvotes	150

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?

Text solutionVerified

Practice questions from similar books

Three horses H1​,H2​,H3​ entered a field which has seven portions marked P1​,P2​,P3​,P4​,P5​,P6​ and P7​. 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?

Text solutionVerified

Practice questions from similar books

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?