How many ways are there to select 4 people from a group of 8 people and award them first through fourth prizes?
The number of ways of selecting four people from a group of eight people is given by the combination formula, which is denoted by C(8,4) or 8C4.
C(8,4) = 8! / [(8-4)! * 4!] = 8! / 4!4! = (8 × 7 × 6 × 5) / (4 × 3 × 2 × 1) = 70
Once we have selected four people, there are 4! ways of awarding them the first through fourth prizes.
Therefore, the total number of ways to select 4 people from a group of 8 people and award them first through fourth prizes is:
C(8,4) × 4! = 70 × 24 = 1680.
So, there are 1680 distinct ways to select 4 people from a group of 8 people and award them first through fourth prizes.