All face cards from a pack of 52 playing card | vedclass

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Question

(A) Total cards after removing face cards $= 52 - 12 = 40$.The total number of ways to draw two cards from $40$ is $^{40}C_{2} = \frac{40 	imes 39}{2

Vedclass · Accepted Answer

$\frac{1}{13}$

Vedclass · Answer

(A) Total cards after removing face cards $= 52 - 12 = 40$.The total number of ways to draw two cards from $40$ is $^{40}C_{2} = \frac{40 	imes 39}{2} = 780$.There are $10$ denominations remaining (Ace,$2, 3, 4, 5, 6, 7, 8, 9, 10$).For each denomination,there are $4$ cards available. The number of ways to choose a pair of the same denomination is $^{4}C_{2} = 6$.Since there are $10$ such denominations,the total favorable ways $= 10 	imes 6 = 60$.The probability is $\frac{60}{780} = \frac{6}{78} = \frac{1}{13}$.

All face cards from a pack of $52$ playing cards are removed. From the remaining $40$ cards,two are drawn randomly without replacement. The probability of drawing a pair (cards of the same denomination) is:

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