Question

Considering 6 cards fr a pack of cards without replacement . What is the probability that 3 of the cards will be black?

Answer 1

3 of the cards will be black and 3 of the cards will be red

$$P(3\ black \ and\ 3\ red)=\dfrac{\dbinom{26}{3}\dbinom{26}{3}}{\dbinom{52}{6}}=$$

$$=\dfrac{\dfrac{26!}{3!(26-3!)!}\cdot\dfrac{26!}{3!(26-3)!}}{\dfrac{52!}{6!(52-6)!}}=$$

$$=\dfrac{26(25)(24)(26)(25)(24)(120)}{52(51)(50)(49)(48)(47)(6)}=$$

$$=\dfrac{13000}{39151}\approx0.332048$$