Suppose 4 cards are chosen at random from a deck of 52. What is the probability that all four cards are A,J,Q,K or heart?
So what I did is decide each of the 4 card types has 4 cards and the hearts have 13 cards but 4 of these cards can overlap because of the suits. So by using inclusion exclusion I took (4 x 4) + 13 - 4 = 25 .
My final answer is: P(E) = ${C(25, 4)}/{C(52, 4)}$ Is this correct?
Thank you for help in confirming.
Yes, it is correct. Alternatively: $$P=\frac{25}{52}\cdot \frac{24}{51}\cdot \frac{23}{50}\cdot \frac{22}{49}.$$ which conforms with your answer.