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?
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:
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.
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.
Since each selection is independent and order matters, we multiply the number of choices at each step:
There are
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.Tips for related online calculators
You need to know the following knowledge to solve this word math problem:
combinatoricsGrade of the word problem
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