If you are dealt 55 cards from a shuffled deck of 52 cards, find the probability of getting threethree queensqueens and twotwo kingskings.

We need to find the probability of getting 3 queens and 2 kings

In 52 cards, we have 4 queens and 4 kings

We need to select 3 queens from 4 queens

/[/frac{n!}{r! (n-r) !}/]

So different combinations of selecting 3 queens from 4 queens is 4C3

/[/frac{4!}{3! (4-3) !}/] = 4

We need to select 2 kings from 4 kings

/[/frac{n!}{r! (n-r) !}/]

So different combinations of selecting 2 kings from 4 kings is 4C2

/[/frac{4!}{2! (4-2) !}/] = 6

Total combination of selecting 5 cards from 52 cards = 52C5

/[/frac{52!}{5! (52-5) !}/] = 2598960

Probability of getting 3 queens and 2 kings = 4C3 * 4C2 / 5C52

/[/frac{4*6}{2598960}/]

1 / 108290