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Class 11MathematicsPermutations and CombinationsCombinationsExpert
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From a deck of (52) cards, (5) cards are chosen with exactly (2) kings. How many hands are possible?

Answer and explanation

Correct answer: (103776)

The selection is ( \binom{4}{2}\binom{48}{3}=103776 ). For exactly-type questions, choose special objects first and then the remaining objects.

Related tags

Class11CombinationsCardsExactlyExpertPermutations And CombinationsMathematicsClass 11 Mcq
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  2. 2A student chooses one subject from 3 subjects and one game from 5 games. How many different selections are possible in total?
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  4. 4An examination contains 6 short-answer questions and 4 long-answer questions. A student has to solve exactly one of them. In how many ways can the student choose the question?
  5. 5A meal plate offers 2 bread choices, 3 vegetable choices, and 2 dessert choices. In how many ways can a plate be prepared by choosing one item from each category?
  6. 6A bag contains pens in 3 different colors, markers in 4 different colors, and pencils in 2 different colors. In how many ways can one pen, one marker, and one pencil be chosen?
  7. 7A vehicle number consists of two letters followed by two digits. There are 4 choices for each letter and 10 choices for each digit. If repetition of letters and digits is allowed, how many distinct vehicle numbers can be formed?
  8. 8A bag has 6 red and 5 blue balls. Four balls are to be selected with equal numbers of both colours. How many selections are possible?
  9. 9If \(\frac{(n+2)!}{(n-2)!}=3024\), what is the value of \(n\)?
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