Step-by-step explanation:
The first chair can be sat in by any of the 8 people. The second can then be sat in by any of the 7 people left after one sits in the first chair. The third chair has 6 choices, the fourth 5 and the fifth 4. 8*7*6*5*4.
Alternately, choose 5 of the 8 people, and arrange them in the 5 chairs. You choose 5 from 8 as (85)=8!(8–5)!∗5! and you arrange 5 things in 5! ways. So (85)∗5!=8!(8–5)!∗5!∗5!=8!∗5!3!∗5!=8!3!=8∗7∗6∗5∗4=P(8,5)
