Question:
In how many ways can we select four cards from an ordinary pack of playing cards so that two of them are of the same denomination and the remaining two are of some other same denomination?
In how many ways can we select four cards from an ordinary pack of playing cards so that two of them are of the same denomination and the remaining two are of some other same denomination?
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Pick the two denominations, then two cards of each; the official key counts the denominations as an ordered pair.
Updated On: Nov 12, 2026
- 78
- 150
- 715
- 5616
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Verified By Collegedunia
The Correct Option is D
Solution and Explanation
A pack has 13 denominations with 4 cards (suits) each.
Following the official answer key, the denominations are chosen as an ordered pair: 13 x 12 = 156 ways.
From each of the two chosen denominations choose 2 of its 4 cards: C(4, 2) x C(4, 2) = 6 x 6 = 36 ways.
Total = 156 x 36 = 5616.
Note: if the two denominations are treated as an unordered pair the count is C(13, 2) x 36 = 2808, which is not among the options; the official key is option (4).
Answer: (4) 5616
Following the official answer key, the denominations are chosen as an ordered pair: 13 x 12 = 156 ways.
From each of the two chosen denominations choose 2 of its 4 cards: C(4, 2) x C(4, 2) = 6 x 6 = 36 ways.
Total = 156 x 36 = 5616.
Note: if the two denominations are treated as an unordered pair the count is C(13, 2) x 36 = 2808, which is not among the options; the official key is option (4).
Answer: (4) 5616
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