Question

From a pack of cards 3 cards are drawn what is the probability that it has on e jack, one ace and one king

Answer 1

Lets keep this simple.

Deck of cards = 52 cards. There are 4 Aces (A), 4 Kings(K) & 4 Jacks(J) in the deck.

Three cards drawn can be AJK, AKJ, KAJ, KJA, JAK, JKA (That's 6 combinations)

Probability = 6 x 4/52 x 4/51 x 4/50

= 384/132600 which simplifies to 16/5525

Or 0.00289 (~0.29%)

(Note that we decrease total outcomes to 51, when one card is drawn, and to 50, when two cards were already drawn, leaving behind 50 cards)

Another alternative:

Three cards can be drawn from a pack of cards in 52C3 ways.

There are 4 Aces, 4 Kings, and 4 Jacks in a pack of cards.

An Ace can be drawn in 4C1 ways
A King can be drawn in 4C1 ways
A Jack can be drawn in 4C1 ways

Required Probability = [ 4C1 x 4C1 x 4C1 ] / [ 52C3 ]

I will leave the calculation part to You ;)

The first two mathods above used combinations. You can also use the laws of probability. First we calculate the probability that the first card is an ace, the second a king and the third a jack: 4/52 * 4/51 * 4/50 = 64/132600. (The second and third factors are conditional probabilities). It is easy to see that the same probability applies to any order of drawing  and we may add these probabilities. As there are 6 possible orders, the answer is 6 * 64/132600 = 64/22100 = 16/5525.

Hope This Helps :)