SOLUTION: Could you please help me with the following question? A doctor visits 5 people by bus once a day. He can use either of two buses, but once he starts out he visits all 5 people

Algebra ->  Permutations -> SOLUTION: Could you please help me with the following question? A doctor visits 5 people by bus once a day. He can use either of two buses, but once he starts out he visits all 5 people       Log On


   

Question 253885: Could you please help me with the following question?
A doctor visits 5 people by bus once a day. He can use either of two buses, but once he starts out he visits all 5 people in the .
same order before returning home. How many possibilities are there?

Thank you
Found 2 solutions by jim_thompson5910, richwmiller:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Since order matters, he has 5 choices for the first patient, 4 for the second (since he can't see the same person twice), 3 for the third, 2 for the fourth, and one for the fifth.

Multiply these choices out to get 5*4*3*2*1=120


So there are 120 different possibilities.


Alternatively, you can use the permutation formula P%28n%2Cr%29=n%21%2F%28n-r%29%21 with n=5 and r=5 to get P%285%2C5%29=5%21%2F%285-5%29%21=5%21%2F0%21=%285%2A4%2A3%2A2%2A1%29%2F1=120%2F1=120 and you'll get the same answer

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
First of all i would like to meet this doctor who takes the bus!
Second I would like to meet a doctor who visits homes!
This person is not in the USA for sure!
It sounds like their are basically only two choices . Which bus?
If I am reading it right, he follows the same route visiting patients no matter which bus he takes.