Problema Solution
an experiment consist of dealing 7 cards from a standard form 52-card deck. what is the probability of being dealt exactly 4 faces cards?
Answer provided by our tutors
we will assume that the order of the dealing doesn't matter
the total number of face cards is: 3*4 = 12 card
P(exactly 4 face cards) = C(12, 4)/C(52, 7)
where C(n, k) = n!/(k!(n - k)!) is the number of k-combinations from a given set of n elements
C(12, 4) = 12!/((12 - 4)! 4!) = 12!/(8! 4!) = 9*10*11*12/(2*3*4) = 495
C(52, 7) = 52!/((52 - 7)! 7!) = 52!/(45! 7!) = 46*47*48*49*50*51*52/(2*3*4*5*6*7) = 133784560
P(exactly 4 face cards) = 495/133784560
P(exactly 4 face cards) = 0.0000037