The posted problem has been transcribed from the original source -- the book
GMAT for Dummies -- incorrectly.
In the book, the prompt reads as follows:
Gmat_mission wrote:A lawn care company has five employees, and there are ten houses that need care on a given day. How many different ways can the company assign the five employees to work at the different houses on that day if each employee provides service for just one home?
(A) 50
(B) 2!/1!
(C) 120
(D) 10!/5!
(E) 10!
Number of houses that could be assigned to the first employee = 10. (Any of the 10 houses.)
Number of houses that could be assigned to the second employee = 9. (Any of the 9 remaining houses.)
Number of houses that could be assigned to the third employee = 8. (Any of the 8 remaining houses.)
Number of houses that could be assigned to the fourth employee = 7. (Any of the 7 remaining houses.)
Number of houses that could be assigned to the fifth employee = 6. (Any of the 6 remaining houses.)
To combine these options, we multiply:
10*9*8*7*6.
The product above is equivalent to
D:
10!/5! = 10*9*8*7*6.
The correct answer is
D.
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