As shown above, a classic deck of playing cards is made up of 52 cards, 26 of which are black and the other 26 are red. Each color is split into two suits of 13 cards each (clubs & spades are black, and hearts & diamonds are red). Each suit is split into 13 ranks of cards (Ace, 2-10, Jack, Queen, and King). If you select a card at random, what is the probability of getting... (a) ...a 6 of Diamonds? (b) ...a Heart or Diamond? (c) ...a number smaller than 3 (counting the ace as a 1)? Give all your answers as reduced fractions.
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.
As shown above, a classic deck of playing cards is made up of 52 cards, 26 of which are black and the other 26 are red. Each color is split into two suits of 13 cards each (clubs & spades are black, and hearts & diamonds are red). Each suit is split into 13 ranks of cards (Ace, 2-10, Jack, Queen, and King).
If you select a card at random, what is the
(a) ...a 6 of Diamonds?
(b) ...a Heart or Diamond?
(c) ...a number smaller than 3 (counting the ace as a 1)?
Give all your answers as reduced fractions.
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