Suppose you choose 9 cards from a standard 52-card deck (with 13 hearts, 13 spades, 13 clubs and 13 diamonds). How many different choices of cards are possible if at most two cards must be clubs? you must choose two clubs and four diamonds? you must choose no hearts and no clubs? you must choose at least four spades and at least three hearts?
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
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Suppose you choose 9 cards from a standard 52-card deck (with 13 hearts, 13 spades, 13 clubs and 13 diamonds). How many different choices of cards are possible if
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at most two cards must be clubs?
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you must choose two clubs and four diamonds?
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you must choose no hearts and no clubs?
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you must choose at least four spades and at least three hearts?
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