six people board a train in which there are eight seats:four on the left and four on the right. In how many ways can they be seated if:?

Question

1) they can sit in any seat

2) if two particular people want to be on the left and one particular person wants to be on the right

please help with working!

Puzzling · Accepted Answer

PART 1:

The first person has 8 choices
The second person has 7 choices
The third person has 6 choices
The fourth person has 5 choices
The fifth person has 4 choices
The sixth person has 3 choices

8P6 = 8 x 7 x 6 x 5 x 4 x 3
= 8! / 2!
= 20,160 ways

PART 2:

The first picky person has 4 seats to choose from on the left
The second picky person has 3 seats to choose from on the left
The third picky person has 4 seats to choose from on the right
The fourth person has 5 remaining seats to pick from
The fifth person has 4 choices
The sixth person has 3 choices

4 x 3 x 4 x 5 x 4 x 3
= 2,880 ways

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six people board a train in which there are eight seats:four on the left and four on the right. In how many ways can they be seated if:?

1 Answer