Combinatorics - 1 Combinatorics The first basic principle...

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1. Combinatorics. The first basic principle is to multiply. Suppose we have 4 shirts of 4 different colors and 3 pants of different colors. How many possibilities are there? For each shirt there are 3 possibilities, so altogether there are 4 × 3 = 12 possibilities. Example. How many license plates of 3 letters followed by 3 numbers are possible? Answer. (26) 3 (10) 3 , because there are 26 possibilities for the first place, 26 for the second, 26 for the third, 10 for the fourth, 10 for the fifth, and 10 for the sixth. We multiply. How many ways can one arrange a, b, c ? One can have abc, acb, bac, bca, cab, cba. There are 3 possibilities for the first position. Once we have chosen the first position, there are 2 possibilities for the second position, and once we have chosen the first two possibilities, there is only 1 choice left for the third. So there are 3 × 2 × 1 = 3! arrangements. In general, if there are n letters, there are n ! possibilities.
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