Discrete Mathematics and Its Applications with MathZone

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ICS 6D ( Discrete Mathematic): Solution to Homework #7 Section 5.3 Disclaimer: There are usually many ways to count the same thing, so here are just some ways and you might come up with a different one, just as good. Although be critical and if you come with something else, make sure it comes out to the same thing, and try to understand why or why not! 2. P (7) = 7! 6. You have to compute these yourself! 8. P (5), it’s the number of orderings, i.e. permutations, among 5 elements. 12. a) C (12 , 3), number of 3-element subsets in 12-element set, because there are 12 indices and you have to pick exactly three where you’ll place a one. b) C (12 , 0) + C (12 , 1) + C (12 , 2) + C (12 , 3), treating bitstrings with exactly zero, one, two, or three ones independently. c) 12 i =3 C (12 , i ), which is equal to 2 12 - ( C (12 , 0) + C (12 , 1) + C (12 , 2)). d) C (12 , 6), because there has to be exactly six ones (and six zeros). 16. You can just add them up: C (10 , 1) + C (10 , 3) + C (10 , 5) + C (10 , 7) + C (10 , 9). You might also be able to do something more clever by comparing the odd-element subsets and even-
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