Question

A deck of cards contains 24 cards where 4 are red. If 6 cards are drawn at random without replacement from this deck, what is the probability that no red cards are drawn?

Answer 1

6 cards out of 24 can be chosen in $n = C_{24}^6$ ways.

6 cards out of 20 non-red can be chosen in $m = C_{20}^6$ ways.

then wanted probability is $p = \frac{m}{n} = \frac{{C_{20}^6}}{{C_{24}^6}} = \frac{{20!}}{{6! \cdot 14!}} \cdot \frac{{6! \cdot 18!}}{{24!}} = \frac{{510}}{{1771}}$

Answer: $p = \frac{{510}}{{1771}}$