I am a little confused at how to solve the Permutations

In summary, the problem is asking for the number of ways five distinct Martians, ten distinct Vesuvians, and eight distinct Jovians can wait in line without any two Martians standing together. The correct calculation would be P(19,5) = 1,395,360 as there are 19 possible spots for the five Martians to fit into the line of 18 Vesuvians and Jovians.
  • #1
Bucs44
57
0
I am a little confused at how to solve the following problem:

In how many ways can five distinct Martians, ten distinct Vesuvians, and eight distinct Jovians wait in line if no two Martians stand together?


What is throwing me off is the addition of another group - if it was just Martians and Vesuvians it would be easy. My guess is P(10,5) = (10*9*8*7*6)

Am I correct or did I mess this up?
 
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  • #2
It doesn't matter how the Vesuvians and Jovians stand so thinking of these as ALIENS you DO have two groups 5 Martians and 18 ALIENS
 
  • #3
So my calculation was wrong? It should be P(18,5) ?
 
  • #4
How many ways could you arrange the ALIENS? Remember they are all distinct.

How many ways could you then slot in the Martians to meet the conditions?
 
  • #5
Right - Because there are 18 Vesuvians and Jovians, the Martians can either fit in the front of the line, middle or end of the line. In which case there would be 19 spots where they could fit in line. P(19,5) = 1,395,360
 
  • #6
Bucs44 said:
Right - Because there are 18 Vesuvians and Jovians, the Martians can either fit in the front of the line, middle or end of the line. In which case there would be 19 spots where they could fit in line. P(19,5) = 1,395,360

Is this right?
 

1. How do I know when to use permutations?

Permutations are used when you want to determine the number of ways a set of objects can be arranged in a particular order. This is different from combinations, where the order does not matter.

2. Can you provide an example of a permutation problem?

Sure, let's say you have 3 different colored marbles and you want to know how many ways you can arrange them in a row. The possible permutations would be red, blue, green; red, green, blue; blue, red, green; blue, green, red; green, red, blue; and green, blue, red. So there are 6 different ways to arrange the 3 marbles.

3. How do I calculate the number of permutations?

The formula for calculating permutations is n! / (n-r)!, where n is the number of objects and r is the number of objects in each permutation. For example, if you have 6 different books and you want to know how many ways you can arrange 3 of them on a shelf, the calculation would be 6! / (6-3)! = 6! / 3! = 6 * 5 * 4 = 120 possible permutations.

4. Can permutations be used for repeating objects?

Yes, permutations can be used for repeating objects. For example, if you have the letters A, B, and B and you want to know how many ways you can arrange them, the possible permutations would be ABB, BAB, and BBA.

5. Are there any shortcuts for solving permutation problems?

Yes, there are a few shortcuts that can be used to solve permutation problems. One is the factorial notation, where n! means n x (n-1) x (n-2) x ... x 3 x 2 x 1. Another is the use of the multiplication principle, which states that if there are n ways to do one task and m ways to do another task, then there are n x m ways to do both tasks together.

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