MATH 310 Homework 1Due January 29, 2021Combinatorial techniques must be used to receive credit. Answers unsupported by work or derived fromlisting every possible outcome will not receive credit.1.There are 10 people at a meeting. Each person is handed a nametag at random. Assumeeveryone has a different name.a.How manytotaldistributions of nametags are possible?b.How many ways can everyoneget the correct nametag?c.How many ways canat least one persongetan incorrect nametag?2.How many5-digit numbers (leading zeros are allowed)contain exactly one 3, one 4, and one 5digits?3.Find the number of ways of factoring8400into two factors,mandn, such thatm> 1,n> 1,the only common divisor ofmandnis 1, i.e.mandnare relatively prime. (For example,8*10504.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 understoodasand.)