1. ## Permutations/Combinations

Hello,

I would like some guidance or help with questions b and c below please. Any assistence will be appreciate. Thanks in advance!

a. In how many ways can 6 people be lined up to get on a bus?
My answer: 6!, or put another way, 6 * 5 * 4 * 3 * 2 * 1 = 720 ways.

b. If 3 specific persons, among 6, insist on following each other, how many ways are possible?
c. If 2 specific persons, among 6, refuse to follow each other, how many ways are possible?

2. b. Tie the 3 specific people together. We can arrange them in 6 different ways. But we can also arrange them all in 24 different ways.

24*6=144 ways

c. tie the two people together and we can arrange them in 2 ways. We can arrange them all in 5! or 120 ways.

120*2=240.

But they DO NOT want to be together: 720-240=480 ways.

How did you get 24 in your workings for question b?

I tied the three people together as you suggested (A, B and C) and I got 42. Here is my logic and working below. Tell me where I went wrong:

1. 2. 3. 4.
A D D D
B A E E
C B A F
D C B A
E E C B
F F F C

1.
A, B & C = 3!
D, E & F = 3!
Sub total = 12 possible ways

2.
A,B & C = 3!
D = 1!
E & F = 2!
Sub total = 9 possible ways

3.
A, B & C = 3!
D & E = 2!
F = 1!
Subtotal = 9 possible ways

4.
A, B & C = 3!
D, E & F = 3!
Subtotal = 12 possible ways

Grand total: 42 possible ways

4. Regarding question C, I got 208. Here is my logic and workings. Let me know where I went wrong. Thanks again.

1 2 3 4
A A A A
C C C C
B D D D
D B E E
E E B F
F F F B

5 6 7 8
B B B B
C C C C
A D D D
D A E E
E E A F
F F F A

1 - 4 =
4! + 4! + 4! + 4! + 1! + 1! + 1! + 1! + 1! + 1! + 1! + 1! = 104 possible ways

plus
5 - 8 =

4! + 4! + 4! + 4! + 1! + 1! + 1! + 1! + 1! + 1! + 1! + 1! = 104 possible ways

Grand total = 208 possible ways

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# in how many ways can 6 people line up to get a bus

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