Permutations (1 Viewer)

[goobi]

A minibus has 6 forward facing and 2 backward facing seats. If 8 people use the bus, in how many ways can they be seated
(a) if 1 person must sit in a forward facing seat
(b) if 2 people must sit in a forward facing seat?

Thanks in advance

 

[Shadowdude]

A minibus has 6 forward facing and 2 backward facing seats. If 8 people use the bus, in how many ways can they be seated
(a) if 1 person must sit in a forward facing seat
(b) if 2 people must sit in a forward facing seat?

Thanks in advance

a) One person must sit in a forward facing seat.

1. Place the person who must sit in a forward facing seat... 6 ways
2. Place the other seven people in the remaining 7 seats... 7! ways

Ans: 6*(7!)

b) Two people must sit facing forward

1. Place two people who must sit in a forward facing seat... C(6,2) ways ("6C2")
2. Place the other 6 people in the remaining seats... 6! ways

Ans: C(6,2)*6!


It's late so... that could be wrong. What are the answers in the back of the book?

 

[goobi]

a) One person must sit in a forward facing seat.

1. Place the person who must sit in a forward facing seat... 6 ways
2. Place the other seven people in the remaining 7 seats... 7! ways

Ans: 6*(7!)

b) Two people must sit facing forward

1. Place two people who must sit in a forward facing seat... C(6,2) ways ("6C2")
2. Place the other 6 people in the remaining seats... 6! ways

Ans: C(6,2)*6!


It's late so... that could be wrong. What are the answers in the back of the book?

Your first answer is correct.

However, the second one should be 21600 as shown at the back of the book.

BTW thanks for your help

 

[goobi]

a) One person must sit in a forward facing seat.

b) Two people must sit facing forward

1. Place two people who must sit in a forward facing seat... C(6,2) ways ("6C2")
2. Place the other 6 people in the remaining seats... 6! ways

Ans: C(6,2)*6!

I think we should use permutations here as the order does matter.
So, the answer should be 6P2*6! ways = 21600

 

[D94]

There's a reason as to why it's permutations. You arrange the 2 forward sitting people 6C2 ways, but those two people can be arranged 2! ways, which is essentially 6P2, and then you multiply by the 6!.

 

[Shadowdude]

Aha, I knew I did something wrong. Oh well, moral of the story: don't do maths at midnight

 

[fx82au]

11 years later, and i thank you for not making me go crazy trying to answer these questions. thankyou fellow humans