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junior college 2 | H2 Maths
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Kimberly (Hui Jing)
Kimberly (Hui Jing)

junior college 2 chevron_right H2 Maths chevron_right Singapore

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: 5 years ago
Views: 325
J
J
5 years ago
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
Kimberly (Hui Jing)
Kimberly (Hui Jing)
5 years ago
thank you again J!
J
J
5 years ago
Welcome. Slight amendment to the explanation, do take a look

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Keith Lee
Keith Lee's answer
258 answers (Tutor Details)
1st
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.
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Kimberly (Hui Jing)
Kimberly (hui Jing)'s answer
8 answers (Tutor Details)
another clear explanation in the comments!!^