a standard deck of 52 playing cards contains four of each numbered card 2 - 10 and four each of aces, kings…

a standard deck of 52 playing cards contains four of each numbered card 2 - 10 and four each of aces, kings, queens, and jacks. two cards are chosen from the deck at random. which expression represents the probability of drawing a king and a queen?\n\\(\\frac{(_{4}p_{1})(_{3}p_{1})}{_{52}p_{2}}\\)\n\\(\\frac{(_{4}c_{1})(_{3}c_{1})}{_{52}c_{2}}\\)\n\\(\\frac{(_{4}p_{1})(_{4}p_{1})}{_{52}p_{2}}\\)\n\\(\\frac{(_{4}c_{1})(_{4}c_{1})}{_{52}c_{2}}\\)

a standard deck of 52 playing cards contains four of each numbered card 2 - 10 and four each of aces, kings, queens, and jacks. two cards are chosen from the deck at random. which expression represents the probability of drawing a king and a queen?\n\\(\\frac{(_{4}p_{1})(_{3}p_{1})}{_{52}p_{2}}\\)\n\\(\\frac{(_{4}c_{1})(_{3}c_{1})}{_{52}c_{2}}\\)\n\\(\\frac{(_{4}p_{1})(_{4}p_{1})}{_{52}p_{2}}\\)\n\\(\\frac{(_{4}c_{1})(_{4}c_{1})}{_{52}c_{2}}\\)

Answer

Explanation:

Step1: Calculate number of ways to choose a king and a queen

There are 4 kings and 4 queens in a deck. The number of ways to choose 1 king out of 4 is ${4}C{1}$, and the number of ways to choose 1 queen out of 4 is ${4}C{1}$. By the multiplication - principle, the number of ways to choose a king and a queen is $({4}C{1})({4}C{1})$.

Step2: Calculate number of ways to choose 2 cards from 52

The number of ways to choose 2 cards from a deck of 52 cards is ${52}C{2}$.

Step3: Calculate the probability

The probability of an event is the number of favorable outcomes divided by the number of total outcomes. So the probability of drawing a king and a queen is $\frac{({4}C{1})({4}C{1})}{{52}C{2}}$.

Answer:

$\frac{({4}C{1})({4}C{1})}{{52}C{2}}$