If you are dealt five cards from a shuffled deck of 52 cards find the probability of getting three queens and two kings

The probability of getting three queens and two kings is

Solution:

Given that , you are dealt five cards from a shuffled deck of 52 cards  

We have to find the probability of getting three queens and two kings  

Now, we know that, in a deck of 52 cards, we will have 4 queens and 4 kings.

Probability of first queen:

Probability of second queen:

Here we used 3 for favourable outcome, since we already drew 1 queen out of 4

And now number of outcomes = 52 – 1 = 51

Probability of third queen:

Similarly here favorable outcome = 2, since we already drew 2 queen out of 4

And now number of outcomes = 51 – 1 = 50

Probability for first king:

Here kings are 4, but overall cards are 49 as 3 queens are drawn

Probability for second king:

Here, kings are 3 and overall cards are 48 as 3 queens and 1 king are drawn

And, finally the overall probability to get 3 queens and 2 kings is:

Hence, the probability is