Ten huskies are to be selected to pull a dogsled. How many different arrangements of the 10 huskies on a dogsled are possible?

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justaguide eNotes educator| Certified Educator

The question is a little vague.

Ten huskies are to be selected to pull a dogsled. The number of ways in which this can be done is dependent on the total number of huskies from which these ten are being selected. If the total number were N, the number of ways of selecting the ten huskies would be given by `NC10 = (N!)/(10!*(N-10)!)`

As we do not have the value of N, we move over to the next part of the question. Ten huskies have been selected to pull the dogsled and now the number of different arrangements of the ten huskies has to be determined.

There are 10 positions in which the huskies can stand. The first position can be filled by any of the 10. Once this is done, the second position can be filled by any of the remaining 9. The next position can be filled by any of the remaining eight. Moving ahead in the same way, by the time we reach the tenth position there is only one husky remaining.

The number of ways of arranging r objects from a set of n is given by nPr which is equal to `(n!)/((n-r)!)`. Here, n = 10 and r is also equal to 10.

`10P10 = (10!)/((10-10!))`

= `(10!)/(0!)`

The value of 0! is 1.

10P10 = 10! = 10*9*8*7...*1= 3,628,800

The total number of different arrangements of the 10 huskies on a dogsled is equal to 3,628,800.