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six horses take part in a race.in how many ways can these horses come in first,second and third place,if a particular horse is among three winners(assuming no ties)?

six horses take part in a race.in how many ways can these horses come in first,second and third place,if a particular horse is among three winners(assuming no ties)?
 

Grade:12

2 Answers

Vijay Mukati
askIITians Faculty 2590 Points
6 years ago
This will be equal to selecting 3 out of 6 and then rearranging them for the different places (6P3). Thanks.
Rajdeep
13 Points
2 years ago
Here no.of horses(objects under consideration)= 6
We know number of permutations when one object is always included is P(n-1, r-1) ×r 
Therefore answer = 5!/(5-2)! ×3 = 60.(Taking n=6 and r=3 as three prizes are there.)

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