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junior college 2 | H2 Maths
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hi hi! I don't know how to do the underlined part.
k=15, m is at least 9. tho I doubt these info would be needed. The given answer is 2! x 2! x 3C2 X 2! x 6 = 144. I understand everything until the "x 6" part why do we need to multiply by 6?
Date Posted: 6 years ago
Views: 361
Allocate Teacher 1 into any seat first. There are 6 distinguishable seats available to choose from → 6 ways to choose.
Now, Teacher 2 cannot be next to Teacher 1, so the two seats adjacent to Teacher 1 cannot be allocated. So there are 3 seats left for teacher 2 to sit on. → 3 ways to choose.
For one of these three ways, you are left with two pairs of seats. So to put the twins, it's 2C1 (two pairs choose one pair).
For the other two ways, there is 1 single seat and 3 adjoining/adjacent seats left .There are only 2 ways to place the twins among these 3 seats. (Eg. Seat 1,2,3, you can only allocate 1,2 or 2,3 since it's a round table)
So total number of ways to allocate twins for each of the three ways is 2.
The twins can be permutated among themselves. So → 2!
Lastly, permutate the swimmer and the badminton player → 2!
So you have 6 x 3 x 2 x 2! x 2! = 144
Now, Teacher 2 cannot be next to Teacher 1, so the two seats adjacent to Teacher 1 cannot be allocated. So there are 3 seats left for teacher 2 to sit on. → 3 ways to choose.
For one of these three ways, you are left with two pairs of seats. So to put the twins, it's 2C1 (two pairs choose one pair).
For the other two ways, there is 1 single seat and 3 adjoining/adjacent seats left .There are only 2 ways to place the twins among these 3 seats. (Eg. Seat 1,2,3, you can only allocate 1,2 or 2,3 since it's a round table)
So total number of ways to allocate twins for each of the three ways is 2.
The twins can be permutated among themselves. So → 2!
Lastly, permutate the swimmer and the badminton player → 2!
So you have 6 x 3 x 2 x 2! x 2! = 144
thank you again J!
Welcome. Slight amendment to the explanation, do take a look
See 2 Answers
done
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To answer your questions, multiply by 6 because of 6 distinguishable seats, so all 6 orientations are different.
Anyway I also provided my answer which may or may not be a different approach to what you know.
Anyway I also provided my answer which may or may not be a different approach to what you know.
Date Posted:
6 years ago
done
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another clear explanation in the comments!!^
Date Posted:
6 years ago
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