How many permutations of simple events

So, there are 4! = 24 ways. For the third part, you can think of it as placing the two people who don't want to be together in the remaining four spots, which can be done in 4C2 = 6 ways.In summary, there are 720 ways to line up 6 people, 24 ways if 3 specific people must follow each other, and 6 ways if 2 specific people must not follow each other. The concept involved in solving the second and third parts is rearranging and grouping individuals.
  • #1
waealu
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Homework Statement



I am stuck on this problem relating to permutations:

The first part asks how many ways can 6 people be lined up. This answer, I believe is 6! = 720 ways.

The second part: If 3 specific persons, among 6, insist on following each other, how many ways are possible?

The third part: If 2 specific persons, among 6, refuse to follow each other, how many ways are possible?

The first part is easy, but I don't know how to do the second and third parts. What is the concept involved in solving the second and third parts?

Thanks for the help!
 
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  • #2
For the second part, just think of the three-people clump as one person, so you have four people that you need to order.
 

FAQ: How many permutations of simple events

How do you calculate the number of permutations of simple events?

The number of permutations of simple events can be calculated using the formula n! / (n-r)!, where n is the total number of events and r is the number of events being selected.

What is the difference between permutations and combinations?

Permutations and combinations both involve selecting items from a larger set, but permutations take into account the order in which the items are selected, while combinations do not. For example, selecting 3 items from a set of 5 can result in 60 permutations (5! / (5-3)!), but only 10 combinations (5! / (3! * (5-3)!)).

Can the number of permutations of simple events be greater than the number of events in the set?

No, the number of permutations of simple events cannot be greater than the number of events in the set. It is possible for the number of permutations to be equal to the number of events, but it cannot exceed it.

How can permutations of simple events be used in real-life situations?

Permutations of simple events can be used in real-life situations to calculate the number of possible outcomes for a given event or situation. For example, a restaurant with 10 menu items could use permutations to determine the number of different combinations of meals that can be made from those items.

Are there any limitations to using permutations for predicting outcomes?

Yes, there are limitations to using permutations for predicting outcomes. Permutations assume that all events are equally likely to occur, which may not be the case in real-life situations. Additionally, permutations do not take into account external factors that may influence the outcomes of events.

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