MAT 521Spring Lecture 3

# MAT 521Spring Lecture 3 - Lecture 3 Section 1.8...

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Lecture 3 Section 1.8: Combinations Definition: Consider a set of n elements. A combination (without replacement) of these n objects taken r at a time is any subset consisting of r elements regardless of order. Example: Let A = {a, b, c, d}. List all the combinations of A taken 2 elements at a time. C n, r = number of combinations of n elements taken r at a time = P n, r /k! = k n C n, r is called the binomial coefficient. Binomial Theorem: For all numbers of x and y and each positive integer n,

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(x+y) n = k n k n 1 k y x k n - = . Example 1.8.1 Selecting a Committee. Suppose that a committee composed of 8 people is to be selected from a group of 20 people. The number of different groups of people that might be on the committee is C 20, 8 = 20!/[(8!)(2!)] = 125970. Example 1.6.3 Genetics. Inherited traits in humans are determined by material in specific locations on chromosomes. Each normal human receives 23 chromosomes from each parent, and these chromosomes are naturally paired, with one chromosome in each pair coming from each parent. For the purpose of this text, it is safe to think of a gene as a portion of each chromosome in a pair. The genes, either one at a time or in combination, determine the inherited traits, such as blood type and hair color. The material in the two locations that make up a gene on the pair of
chromosomes comes in forms call alleles. Each distinct combination of alleles (one on each chromosome) is called a genotype. Consider a gene with only two different alleles A and a. Suppose that both

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## This note was uploaded on 02/17/2011 for the course MAT 521 taught by Professor Staff during the Spring '08 term at Syracuse.

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MAT 521Spring Lecture 3 - Lecture 3 Section 1.8...

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