MATH 310 Homework 1Due January 29, 2020Combinatorial techniques must be used to receive credit. Answers unsupported by work or derived fromlisting every possible outcome will not receive credit.1.Fifteen people each bring one dog to the dog park. Find the number of ways of choosing a dogand a person such that:a.Each dog belongs to the person,b.Each dog does not belong to the person.2.How many among the first 100,000 positive integers contain exactly one 3, one 4, and one 5 intheir decimal representation?3.Find the number of ways of factoring 441,000 into two factors,mandn, such thatm> 1,nand the only common divisor ofmandnis 1, i.e.mandnare relatively prime. (For example,8*55125.)4.There are 10 members –A,B,C,D,E,F,G,H,I, andJ– in the executive council of a club. Thecouncil has to choose a chair, a secretary, and a treasurer among themselves. It is understood> 1,