Question

Compute the probability of randomly drawing five cards from a deck and getting 3 Aces and 2 Kings

Answer 1

 

The number of ways of getting 3 Aces and 2 Kings is (4C3)(4C2) = 24  

The number of ways of drawing 5 cards from a deck of 52 cards is 52C5 = 2598960  

P = 24/2598960 = 1/108290

Answer 2

Given,

Number of cards drawn randomly = 5

Total cards in the deck = 52

To Find,

Probability of getting 3 aces and 2 kings =?

Solution,

Number of aces in the deck = 4

Number of kings in the deck = 4

Total number of observations = 56C5 = 2598960

Probability of getting 3 aces and 2 kings = (4C3 * 4C2) / 56C5

Probability of getting 3 aces and 2 kings = (4 * 6) / 2598960

Probability of getting 3 aces and 2 kings = 24 / 2598960

Hence, probablity is  24 / 2598960.