Description
Dale Klitzke is a milk truck driver for Swiss Valley Farms Cooperative in eastern Iowa. Dale has to start at the processing plant and pick up milk on 10 different farms. In how many ways can Dale visit each farm and return to the processing plant?
Explanation & Answer
Dale starts from a Processing plant and visits all the 10 different farms and return back to the Processing Plant. since he picks up milk from different farms, each farm can be visited by him only once.
1. Firstly Dale had the chance to visit any of the 10 farms, so number of choices of farm are 10
2.Since one of the farms is already visited, the next visit can only be to the remaining 9 farms, so number of chioces of farm are 9.
3.Since 2 farms are already visited, the next visit can only be to the remaining 8 farms, so number of choices of farm are 8
4. Since 3 farms are already visited, the next visit can only be to the remaining 7 farms, so number of choices of farm are 7
5.Since 4 farms are already visited, the next visit can only be to the remaining 6 farms, so number of choices of farm are 6
6. Since 5 farms are already visited, the next visit can only be to the remaining 5 farms, so number of choices of farm are 5
7. Since 6 farms are already visited, the next visit can only be to the remaining 4 farms, so number of choices of farm are 4
8. Since 7 farms are already visited, the next visit can only be to the remaining 3 farms, so number of choices of farm are 3
9. Since 8 farms are already visited, the next visit can only be to the remaining 2 farms, so number of choices of farm are 2
10. Since 9 farms are already visted, the next visit can only be to the remaining 1 farms.
Since Each Farm will be attened by Dale only once, no of ways from last visited Farm to Processing plant = 1
So the Total Number of ways Dale can visit each Farm and return to the processing plant are = 10 Factorial ways which will be Equal to 10* 9* 8* 7* 6* 5* 4* 3* 2* 1* 1 = 3628800 ways
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