Wording in a Permutation/Combination Problem

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In summary, the conversation is discussing the question of how many 4-digit codes can be formed by choosing 4 numbers from 0-9 if the numbers cannot be repeated. The participants are trying to clarify the meaning of "if number cannot be the same" and agree that it likely refers to the concept of permutation.
  • #1
mwang
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Hello all,

I came across a question regarding permutations that I found a bit confusing. Please tell me what you think it means

"Choose 4 numbers from 0-9 to comprise a 4-digit code.

1) If number cannot be the same, how many codes can we have"

The way I see it, it means that the digits in the codes cannot be repeated. So basically, the possible codes cannot be 2223; all the digits must be different. Is this what you think too?

Thanks
 
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  • #2
I can't imagine what "if number cannot be the same" means, but I think permutation is a reasonable guess. If this is for a class, you can always just explain to the teacher that you didn't understand the question. :smile:
 
  • #3
honestrosewater said:
I can't imagine what "if number cannot be the same" means
It means, "if no two numbers can be the same."
 

What is the difference between a permutation and a combination?

A permutation is an arrangement of objects in a specific order, while a combination is a selection of objects without regard to their order. For example, in a permutation of the letters "ABC", "ABC" and "CAB" would be considered different arrangements. In a combination, these two arrangements would be considered the same.

How do I know when to use a permutation or a combination in a problem?

You should use a permutation when the order of the objects matters in the problem, such as arranging a specific order of people for a race. You should use a combination when the order does not matter, such as selecting a group of people for a committee.

What is the formula for calculating the number of permutations?

The formula for calculating the number of permutations is n! / (n-r)!, where n is the total number of objects and r is the number of objects being selected.

What is the formula for calculating the number of combinations?

The formula for calculating the number of combinations is n! / (r!(n-r)!), where n is the total number of objects and r is the number of objects being selected.

Can I use a calculator to solve permutation/combination problems?

Yes, many scientific and graphing calculators have a built-in function for calculating permutations and combinations. However, it is important to understand the formulas and concepts behind these calculations in order to use the calculator effectively and check for accuracy.

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