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For a particular office telephone, seven telephone calls are randomly received in a week, and these...

For a particular office telephone, seven telephone calls are randomly received in a week, and these calls are randomly distributed among the seven days. What is the probability that no call will be received on exactly one day?

sample space = 7^7

my rationale was that no call received on exactly one day = at least one call on other 6 days and 2 calls on 1 0f the 6 days. So we first do 7C6 to select the days with calls, and then 6C1 to select the day with 2 calls. finally, we do 7C6 x 6C1 x 6P6 to account for the number of ways the calls can be distributed across the 6 days. However, the correct answer should be (6/7)^7 and i'm not sure why. By doing this, does it not take into account that there should be at least one call in 6 of the 7 days?

math   Statistics-And-Probability   
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