Seven cars are in a race there assuming no ties how will be

Seven cars are in a race. there assuming no ties, how will be first place, second place and third place winners many possible results are there for this race ? there are eight people in a math club. an upcoming conference limits attendance to three people per club. how many possible of this math club be chosen to attend the conference?

Solution

a) Total no. of ways = (anyone from 7 can be at 1st place) * (anyone from the remaining 6 can be at 2nd place) * (anyone from the remaining 5 can be at 3rd place)

Total no. of ways = 7*6*5 = 210

b) No. of possible ways = ⁸C₃ = 56