A deck of 52 cards is taken. From this, 4 cards are to be chosen such that exactly two of them are hearts and exactly two of them are kings. In how many ways can this be done?
Solution
Correct Answer: Option B
Exactly two of them are hearts and exactly two of them are kings. This is possible in two ways.
Case i) Out of the 4 cards, no card is a king of hearts.
⇒ Two hearts can be chosen in 12c2 ways, i.e., 66 ways.
And, two kings can be chosen in 3 c2 ways, i.e., 3 ways.
∴ Total numbers of ways in this case = 66 × 3 = 198
Case ii) Out of the 4 cards, one card is a king of hearts.
Now, we have one card fixed. Out of remaining 3 cards, one should be a heart and one should be king. The third card can be any card that is neither king nor heart.
∴ Total numbers of ways in this case = 12 × 3 × (52 – 13 – 3) = 1296
∴ Total number of ways in which it can be done = 198 + 1296 = 1494
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