Problema Solution
A sample of 4 balls is to be selected at random from an urn containing 19 balls numbered 1 to 19. Six balls are green, 5 balls are white, and 8 balls are black.
(a) How many different samples can be selected?
(b) How many samples can be selected that contain at least 1 white ball?
Answer provided by our tutors
(a) How many different samples can be selected?
total number of samples: C(19, 4) = 19!/(4!(19-4)!) = 16*17*18*19/(2*3*4) = 3876
(b) How many samples can be selected that contain at least 1 white ball?
number of samples with not white ball: C(14, 4) = 14!(4!(14-4)!)= 11*12*13*14/2*3*4 = 1001
number of samples with at least one white ball: C(19, 4) - C(14, 4) = 3876 - 1001 = 2875