Question

When three cards are drawn from a standard 52-deck, what is the probability they are all the same rank? (e.g. all three are kings)

Answer 1

No.of favorable outcomes ${=}^4{C}_3\times 13$

any 3 out of 4 one out of 13 nos.

Total no.of outcomes ${}^{52}{C}_3$

$P=\frac{{}^4{C}_3\times 13}{{}^{52}{C}_3}=\frac{4\times 13}{\frac{52\times 51\times 50}{3\times 2\times 1}}$

$=\frac{4\times 13\times 3\times 2\times 1}{52\times 51\times 50}=\frac{1}{425}$