Sequentially pick

There are 6 different tickets marked with numbers 1 to 6 in the pocket.
In how many different ways can we sequentially, taking into account the order, choose three of them, if the chosen tickets return to the pocket?

Final Answer:

n =  216

Step-by-step explanation:

n=63=216



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Showing 2 comments:
Hmp
My reasoning -  There are 6 different tickets. The answer implies that I can choose 3 tickets with the same number. The real answer is 6 x 5 x 4

Dr. Math
To determine the number of ways to sequentially choose 3 tickets from 6 (with replacement and order mattering), we can use the Fundamental Counting Principle.

Solution:


1. First ticket:  
  - There are 6 possible choices (tickets 1 through 6).  
  - The ticket is returned to the pocket, so the pool remains the same for subsequent choices.

2. Second ticket:  
  - Again, 6 possible choices (since the first ticket was returned).  

3. Third ticket:  
  - Once more, 6 possible choices.  

Total number of ordered sequences:


Since each selection is independent and order matters, we multiply the number of choices at each step:
6 × 6 × 6 = 63 = 216

Final Answer:


There are

216

different ways to choose three tickets sequentially with replacement.





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