If you are dealt 6 cards from a shuffled deck of 52 cards fi

If you are dealt 6 cards from a shuffled deck of 52 cards, find the probability of getting three queens and three kings.

Solution

there are total 4 kings and 4 queens in a standard deck

total number of ways of getting 3 kings =4c3 = 4 ways

total number of ways of getting 3 queens = 4c3 = 4 ways

and total ways of getting 6 cards from 52 cards = 52c6 = 20358520

probability pf getting 3 queens and 3 kings = 4*4 / 20358520 = 7.85 * 10^-7