probability

Question

from a well shuffled pack of 52 cards. Three cards are drawn at random. Find the probability of drawing an ace, a king and a jack,

a) 16/5525

b) 16/625

Answer 1

Number of ways of choosing an Ace=$\binom{4}{1}$

Number of ways of choosing a King=$\binom{4}{1}$

Number of ways of choosing a Jack=$\binom{4}{1}$

the number of ways of choosing an Ace, a King and a Jack would be=$\binom{4}{1}$ *$\binom{4}{1}$ * $\binom{4}{1}$= 64

Number of ways of choosing 3 cards from a pack of 52 cards is = $\binom{52}{3}$ =22100

So the probability of drawing an Ace, a King and a Jack =$\frac{64}{22100}$ = $\frac{16}{5525}$

Hence (a) is the Answer.