Transcription of 50 MATHCOUNTS LECTURES (24) COMBINATOTICS BASIC …
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50 MATHCOUNTS LECTURES (24) COMBINATOTICS BASIC …
50 mathcounts lectures (24) COMBINATOTICS 52 BASIC KNOWLEDGE 1. Terms A permutation is an arrangement or a listing of things in which order is important. A combination is an arrangement or a listing of things in which order is not important 2. Definition The symbol ! (factorial) is defined as follows: 0! = 1, and for integers n 1, n!= n (n 1) 1. 1! = 1, 2! = 2 1=2, 3! = 3 2 1=6, 4! = 4 3 2 1 = 24, 5! = 5 4 3 1 1 = 120, 6! = 6 5 4 3 2 1 = 720. 3. Permutations (1). Different elements, with no repetition. Take r elements each time from n distinct elements (1 r n). Number of permutations )!(!),(rnnrnP (1) (2). n distinct objects can be permutated in n! permutations. We let n = r in (1) to get P(n, n) = n! (2) Proof of (2): 50 mathcounts lectures (24) COMBINATOTICS 53 The first object can be chosen in n ways, the second object in n 1 ways, the third in n 2, etc.
50 MATHCOUNTS LECTURES (24) COMBINATOTICS 52 BASIC KNOWLEDGE 1. Terms A permutation is an arrangement or a listing of things in which order is important.
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