MATH239 Lecture : MATH 239 Spring 2014 First Week Course Notes
9 May 2014
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Combinatorics is discrete math dealing with counting questions" and graph theory. How many binary strings of length n are there? : 2n. How many binary strings of length n are there which do not contain the (continuous) substring 0101" ? . How many ways can you make change for a dollar? (in canada! How many k-element subsets are there in an n-element set? : n choose k = n! k! (n k)! How many ways are there to order the numbers from 1 to n with no constraints? : n! Given 123 letters addressed to the 123 students in this class and 123 associated envelopes, how many ways are there to put one letter in each envelope such that nobody gets the right letter? : 123! How many n-polyminos (tetris blocks) are there? : 2 1, 3 2, 4 5|7. How many prime numbers p are there such that p + 2 is also prime? : in nite? e.
