How many ways can 8 people stand in a line if Alice and Bob refuse to stand next to each other?
Answers
Explanation:
There are 6 people that need to sit down, so let’s see how we can fill those 6 seats. We’ll start by finding seats for Alice and Bob. They can’t sit next to each other, so we’ll remove 1 of the seats, seat them both in the remaining 5 seats, then add a seat between them to ensure that they’re not next to each other. There are 5 ways to choose Alice’s seat, and 4 ways to choose Bob’s seat from those that remain, giving 20 ways to seat them.
Once Alice and Bob are seated, we can arrange the remaining people in 4!=24 ways in the other 4 seats, for a total of 20×24=480 ways to seat everyone.
Answer:
There are 35280 ways.
Explanation:
Number of ways 8 people can stand in a line
= 8!
Number of ways 8 people can stand when Alice and Bob always are together = 7!
Therefore,
Required Number = 8! - 7!
= 7 × 7!
= 35280