How do i answer this permutation question?

In summary, the probability of disarming a home security device with 10 buttons by pushing three different buttons in the proper sequence, without pushing any button twice, is 1/720 or 0.14%.
  • #1
Biochemgirl2002
30
1
Question:
A home security device with 10 buttons is disarmed when three different buttons are pushed in the proper sequence. (No button can be pushed twice.) If the correct code is forgotten, what is the probability of disarming this device?

My attempt:

10!/(10-3)! =( 10x9x8x7x6x5x4x3x2x1)/(7x6x5x4x3x2x1)
= 720

therefore there is a 1/720 chance of getting the right combination.

is this correct?

[Moderator's note: Moved from a technical forum and thus no template.]
 
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  • #2
Yes, it looks correct:

you have 10 choices on the first button, 9 choices on the second and 8 choices on the third:

10*9*8 = 720

Hence you have 1/720 or 0.14% chance of getting it right the first time.
 
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Likes Gavran and Biochemgirl2002

1. How do I determine if a problem involves permutations?

Permutations refer to the number of ways a set of objects can be arranged or ordered. If a problem involves finding the number of arrangements or orderings, then it likely involves permutations.

2. What is the formula for finding permutations?

The formula for finding permutations is nPr = n! / (n-r)!, where n represents the total number of objects and r represents the number of objects being arranged or ordered.

3. What is the difference between permutations and combinations?

Permutations take into account the order or arrangement of objects, while combinations do not. For example, the permutations of ABC would include ABC, BAC, and CBA, while the combinations would only include ABC.

4. How do I handle repetitions in permutation problems?

If there are repeated objects in a permutation problem, the formula nPr = n! / (n-r)! may not work. In this case, you can use the formula nPr = n! / (n1! * n2! * ... * nk!), where n1, n2, etc. represent the number of repetitions for each object.

5. Can I use a calculator to solve permutation problems?

Yes, you can use a calculator to solve permutation problems by using the nPr function or by manually entering the formula into the calculator. However, it is important to understand the concept and formula for permutations in order to use the calculator correctly.

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