In a bridge game, a hand consists of 13 cards taken from a deck of 52 cards. (i) A hand is balanced if the number of cards for all suits are almost equal. How many different hands are there, in which we have 4 cards of a certain suit, and 3 cards for each of the other suits? (ii) In bridge games we prefer to have unbalanced hands. How many different hands are there, in which we have 7 cards of the same suit?
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.
In a bridge game, a hand consists of 13 cards taken from a deck of 52 cards.
(i) A hand is balanced if the number of cards for all suits are almost equal. How many different hands are
there, in which we have 4 cards of a certain suit, and 3 cards for each of the other suits?
(ii) In bridge games we prefer to have unbalanced hands. How many different hands are there, in which
we have 7 cards of the same suit?
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