# MATH221 Mathematics for Computer Science | My Assignment Tutor

MATH221 Mathematics for Computer ScienceTutorial Sheet Week 10 – Autumn 20211. How many car number plates are there of the form L1L2L3n1n2n3 where L1; L2; L3 are letters and n1; n2; n3are numbers? If we restrict the possibilities by insisting that there are no repeats, how many are there now?Repeat this question for number plates of the form L1L2n1n2L3L4.2. Currently the U. S. Senate consists of 80 male and 20 female senators. If a committee of 3 senators is formed,what is the probability that it is an all-male committee?3. Give an example of a relation on N [ f0g that is(a) reflexive and transitive, but not symmetric;(b) transitive and symmetric, but not reflexive.4. On R, let the relation R be defined xRy , jx – yj ≤ 1. Prove that R is not an equivalence relation.5. On R2, let the relation R be defined (a; b)R(c; d) , 2a – b = 2c – d. Prove that R is an equivalence relation.Write 3 elements of [(1; 2)].1

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