Question

Find the probability of getting 6 face cards when 6 cards are drawn from a deck without replacement. Enter your answer as a fraction.

Answer 1

The face cards are 4 kings, 4 queens, and 4 jacks, which is equal to 12 face cards.

A deck of cards = 52

Now, the probability is given by the next formula:

`P=\frac{\#\text{ of f}avorable\text{ outcomes}}{Total\text{ of outcomes}}`

In fact, we don't have any orders or replacements.

Therefore:

`P=(12C6)/(52C6)`

The number of favorable outcomes is 12 chose 6 because we are getting 6 cards.

The total number of outcomes is 52 chose 6 because we have drawn 6 cards from the deck.

C means the combination and is calculated by the next formula :

`n\text{Cr}=(n!)/(r!(n-r)!)`

For 12C6:

`12C6=(12!)/(6!(12-6)!)=924`
`52C6=(52!)/(6!(52-6)!)=20358520`

Then:

`P=(154)/(221)`