Given the 16 starting positions in a chessboard, how many ways can you arrange the following: (assuming the same pieces are identical) a. 8 black pawns b. 8 white pawns and 8 black pawns c. 8 black pawns 2 white knights 2 black knights
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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Given the 16 starting positions in a chessboard, how many ways can you arrange the following: (assuming the same pieces are identical)
a. 8 black pawns
b. 8 white pawns and 8 black pawns
c. 8 black pawns 2 white knights 2 black knights
d. 4 white pawns 4 black pawns and a white king
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Prove the following identity:
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