A bucket contains 12 marbles, there are 7 red marbles numbered 1 through 7 and 5 blue marbles numbered 8 through 12. If 6 marbles are pulled from the bucket, determine the number of different 6-sets of marbles that have 3-red and 3-blue marbles. Determine the number of different 3-set or 4-sets of marbles that can be created from this bucket of marbles.
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.
A bucket contains 12 marbles, there are 7 red marbles numbered 1 through 7 and 5 blue marbles numbered 8 through 12.
If 6 marbles are pulled from the bucket, determine the number of different 6-sets of marbles that have 3-red and 3-blue marbles.
Determine the number of different 3-set or 4-sets of marbles that can be created from this bucket of marbles.
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