A group of 10 students consisting of 6 males and 4 females are seated at a round table with chairs of different colours for lunch. Find the number of arrangements such that all the female students are seated together.
Thanks.
10 x 6! x 4!
Choose 6 consecutive seats first,
1 2 3 4 5 6
2 3 4 5 6 7
................
5 6 7 8 9 10
6 7 8 9 10 1
......
10 1 2 3 4 5
There are 10 different ways.
6 men are to sit in these seats. 6! ways.
4 men are to sit in the remaining seats 4! ways.
(7-1)! * 4! * 10 = 172800
My tip: Do as though all chairs are of the same colour, then multiply it by the number of chairs.
At a playground, 3 boys and 6 girls are to be seated round a carousel with 9 numbered seats. Assuming each child occupies exactly one seat, in how many ways can this be done, if the 3 boys must sit together?
Thanks.
3boys form 1 entity. We are left with 7 entities
Step 1: Do unnumbered
(7 - 1)! * 3! = 4320
Step 2: Add in consideration of numbered seats
4320 * 9 = 38880
The solution given was: If the seats are numbered, it is as if they are sitting in a row instead of in a circle, as rotating the whole group results in a new position.
No. of ways = 7! x 3! = 30240
Happened to see this question, which is quite similar to the previous question, but with different workings.
Originally posted by J2011:The solution given was: If the seats are numbered, it is as if they are sitting in a row instead of in a circle, as rotating the whole group results in a new position.
No. of ways = 7! x 3! = 30240
Happened to see this question, which is quite similar to the previous question, but with different workings.
This is a very wrong answer, and it is very misleading. You cannot see it as sitting in a row. This is very very wrong. There will be some solutions missing.
This is a circle question. You are missing the solution where two boys sit at one end and one boy at the other end (if we consider a row). In a circle, they are still considered to be sitting together, but in a row, they are not.
Where did you see this solution?
Just curious, is this a JC question?
Hi granslime.
Yes, PnC is a JC question.
No chance to learn such things in poly. Go uni i sure die liao
It depends on what uni course you are taking. Most courses do not need PnC.
You've pm.