Problema Solution
Have 14 trumpet players, 6 drummers, 4 cymbal players. If 8 is selected what's the probability of only 3 trumpet players
Answer provided by our tutors
The number of all possible selections of 8 people from the set of 14 + 6 + 4 = 24 people is:
C(24, 8) = 24!/((24 - 8)!8!)
C(24, 8) = 24!/(16!8!)
C(24, 8) = 17*18*19*20*21*22*23*24/(2*3*4*5*6*7*8)
C(24, 8) = 735,471
The number of all the possible selections with only 3 trumpets selected is:
C(8, 3)*C((24 - 3),(8 - 3)) = 8!/((8 - 3)!3!) * C(11, 5) = 7*8*(11!/((11-5)!5!)) = 7*8*7*8*9*10*11/(2*3*4*5) = 25,872
The probability p of exactly 3 trumpet players is:
p = 25,872/735,471
p = 0.03518 approximately