A box contains two black balls, labeled 1 and 2, and five white balls, labeled 3, 4, 5, 6, and 7. Alice and Bob each draw two balls from the box, Alice first drawing two balls followed by Bob. If the order of selection matters (that is, Alice drawing 1 2 is different from her drawing 2 1), how many different ways are there for one person to get both black balls?
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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