Permutation problem: Seven friends queue up for a buffet....

In summary, the conversation discusses two different approaches to arranging a group of people into a car with a capacity of 4 or 3 occupants. The first approach involves merging the last two people and arranging the remaining 6 people in 6C4 ways, resulting in 15 possible arrangements. The second approach involves considering the two fellows boarding the car as a group, resulting in 5C2 ways for the remaining 3 people to be arranged, or 5C4 ways for the two fellows and one other person to be arranged, for a total of 15 possible arrangements. The speaker agrees with the second approach.
  • #1
chwala
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Homework Statement
solve the problem below;
Relevant Equations
permutation and combination
1614052420899.png
 
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  • #2
for the first part, not difficult,
we have ##7!=5040##
now for the second part, i get a bit confused here ok, i merged the last two fellows and now i have 6 items...
therefore i will have ##6C4 ##× the remaining ##3## can be arranged in 1 way only= ##15## is this the correct approach?...not one of my favorite topics o0)...

or can i say that, the car can be filled up in this way,
##5C2 ×1## way only(remaining 3 people), assuming that the two fellows board the 4-vehicle capacity or
##5C4 ×1 ##way only(2 fellows plus 1 person) , assuming that the two fellows board the vehicle holding 3 occupants...which gives
##10+5=15##
 
Last edited:
  • #3
I agree with your solution.
 
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Likes chwala

Related to Permutation problem: Seven friends queue up for a buffet....

What is a permutation problem?

A permutation problem is a type of mathematical problem that involves arranging a set of objects or elements in a specific order or sequence. The order of the elements in a permutation is important and can affect the outcome of the problem.

How many possible permutations are there for seven friends queueing up for a buffet?

There are 7! (seven factorial) possible permutations for seven friends queueing up for a buffet. This means that there are 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040 possible ways for the friends to queue up.

What is the formula for calculating permutations?

The formula for calculating permutations is n! / (n-r)! where n is the total number of objects and r is the number of objects being selected. In the case of the seven friends queueing up for a buffet, n = 7 and r = 7, so the formula becomes 7! / (7-7)! = 7! / 0! = 7! = 5040.

What is the difference between a permutation and a combination?

A permutation involves arranging a set of objects in a specific order, while a combination involves selecting a subset of objects from a larger set without regard to order. In the context of the seven friends queueing up for a buffet, a permutation would be the different ways they can stand in line, while a combination would be the different groups of friends that can be formed from the larger group of seven.

How can permutations be used in real-life situations?

Permutations can be used to solve a variety of real-life problems, such as arranging seating at a dinner party, creating unique passwords, or determining the number of possible outcomes in a game or competition. They can also be used in fields such as genetics, computer science, and statistics.

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