How many possible 5-card hands from a standard 52-card deck would consist of the following cards? a) there are __ five-card bands consisting of three clubs and two non-clubs. b) there are __ five-card hands consisting of one face card and four non-face cards. c)there are __ five-card hands consisting of one red card, two spades, and two clubs.
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.
How many possible 5-card hands from a standard 52-card deck would consist of the following cards?
a) there are __ five-card bands consisting of three clubs and two non-clubs.
b) there are __ five-card hands consisting of one face card and four non-face cards.
c)there are __ five-card hands consisting of one red card, two spades, and two clubs.
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