Question

Assume that you have an ordinary deck of 52 playing cards. How many possible 7- card pocker hands are there that contain at least one face card (Jack, Queen, or King)?

Answer 1

There are 115141000 possible ways.

Explanation:

Since it is a 7 – card pocker hands, then the total number of poker hands will be:

`\binom{52}{7}`

Also, the total number of hands without figure cards is

`\binom{40}{7}`

This is because there are 12 cards with figures (4 x J, Q, K).

Therefore, the number of hands with at least one figure will be:

`\binom{52}{7} - \binom{40}{7}`

And this would be

133784560 – 18643560 = 115141000