Khizra K.
1 Expert Answer
Your question is not entirely clear to me. If they insist in being lined up in a specific order there are, in effect, only four objects to be arranged: three individuals and this group, so that would be 4! possible arrangements. 4! = 24 different ways. If they merely insist on being together, but do not care how they are lined up so long as they are together, you would still have four objects 4!, but one of those objects could be in 3! different states. 4!3! = (24)(6) = 144 different ways.
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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?
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?
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.
Thank you for your reply galactus! 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
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
There are
There are
{That is because there are ways to arrange the other 4 people,
ways to arrange the 2 people who refuse to be next to each other,
and places to insert the problem pair in the line formed by tho other 4).
Since
there are ways to line up the 6 people keeping apart the 2 people who refuse to be next to each other.