Question

Suppose that 6 cards are drawn what is the probability that all of them are black

Answer 1

The first card's probability is easy to calculate.
Of the 52 cards, 26 are black, so the probability is
(26 out of 52) or (1 out of 2) or .5

The second card will be drawn from 51 cards of which 25 are black:
25 / 51

Continuing with this pattern, drawing the 3rd card, the probability is
24 / 50

For the 4th card 23 / 49

For the 5th card 22 / 48

For the 6th card 21 / 47

So, to get the probability of drawing all six cards AND getting all black, we multiply these 6 fractions:
probability = (26 / 52) * (25 / 51) * (24 / 50) * (23 / 49) * (22 / 48) * (21 / 47)

probability = 165,765,600 / 14,658,134,400

probability = 0.0113087788306812