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miv72 [106K]
3 years ago
8

A small combination lock on a suitcase has 3 ​wheels, each labeled with the 10 digits from 0 to 9. If an opening combination is

a particular sequence of 3 digits with no​ repeats, what is the probability of a person guessing the right​ combination?
Mathematics
1 answer:
Artyom0805 [142]3 years ago
5 0

Answer:

0.14% probability of a person guessing the right​ combination

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The order in which the numbers are selected is important. For example, 1,3,2 is a different combination than 3,1,2. So we use the permutations formula to solve this question.

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

P_{(n,x)} = \frac{n!}{(n-x)!}

Desired outcomes:

One right combination, so P = 1

Total outcomes:

10 numbers from a set of 3. So

P_{(10,3)} = \frac{10!}{(10-3)!} = 720

What is the probability of a person guessing the right​ combination?

p = \frac{D}{T} = \frac{1}{720} = 0.0014

0.14% probability of a person guessing the right​ combination

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seropon [69]

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b) Use the form (y2-y1)/(x2-x1) where (x1,y1) (x2,y2) are any two points from 2001-2006. It does not matter which points, pick any, and assign each of the numbers x1,y1 and x2,y2. Plug it in to the equation, and simplify. This is your slope, also called m. Now plug m into the equation y-y1=m(x-x1) where y1 and x1 are the x and y coordinates of any point from 2001 to 2006. x and y dont have values themselves, they stay there. Now distribute the m into the parenthesis, add y1 to both sides (to cancel it out on the left), and you should be left with the same equation, but now in y=mx+b form. B is where the line crosses the y axis, so put a point on the vertical axis where b is. M is your slope, so every time you go to the right one number, go up M numbers. Draw another point. Repeat this until you can connect these new dots into a line. This line should be on the same graph as your other points, but might not touch all of the scatter plot points. That's still okay, just leave it as is.

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I hope I have been of some help! Best of luck!!! :)

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Answer:

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Step-by-step explanation:

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