Question

1. Find expressions for each of the following. (Leave your answer as a mathematical expression rather than a number.) (a) The number of strings of 8 lower case letters (a-z) that do not contain any letter more than once. (b) The number of binary strings of length 10 that contain at most two Os. (c) The number of subsets of 11,2,,10 with three elements that contain at least one even number and at least one odd number. [Give brief justifications.]

Answer 1

Choosing lelerWit Cig may centrin O Tu string may cermin 4-zere, , lhatuo pescillein 10Cǐ ways ere even nuuuber ran be slected in c wap and can he put in Ce) an ena c tre places in 3 ways. ne odd nube can be wlected i Cconr and can he ped in ttu rev annin two places in 2 asays. The laat ㅑlace can be İUed uf in 10

1. a) Fra string 4 8 lever case letter, łfu irst grace can be tłud in 26μα .. And 4fa., in 2s wr ance Tu string may cermin 4.zeres, lhat ㅨ pescilde in 10 Ciwayo Eru even nuunbes ran be slectediC) wwp and can be put in an ene c trse places in 3 ways. ne odd nunibe can be wlected in Cconr and can ke pet in tu remainin tve place in 2 esarg. The last place can be Hilsd up in "Gx3ャ"Gx2 t10(. 35, 4.n.puhed ら4x5 + 'Oz all diejenr从k, candi
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