MATH221 Mathematics for Computer ScienceTutorial Sheet Week 9 – Autumn 20211. How many permutations of 3 items taken 5 at a time are there? How many permutations of 5 items taken3 at a time are there?2. A binary word is a word constructed from the alphabet A = f0; 1g. How many binary words of length 5 arethere? How many of these words contain at least one 0 and at least one 1?3. A function from a set A to a set B is a rule that assigns to each a 2 A an element denoted f(a) 2 B. Howmany different functions from fa; b; c; dg to f1; 2; 3g are there?4. In how many ways can a committee of 5 be chosen from 8 people?5. Ten points are marked on the circumference of a circle.(i) How many chords can be formed by joining them in all possible ways?(ii) How many triangles can be formed by joining them in all possible ways?(iii) How many hexagons can be formed by joining them in all possible ways?6. Determine the size of the smallest set having at least 100 proper, nonempty subsets.7. In how many ways can a selection of at least one book be made from 8 books?8. Simplify P13 r=0(-1)r13 r 513-r.9. In a light bulb production factory, 12% of light bulbs were found to be faulty. If three light bulbs are tested,find the probability (as a decimal rounded to four places) that:(a) all three are faulty(b) none is faulty(c) one is faulty.10. A political candidate runs for two offices, A and B. The probability that the candidate wins A is 0.70, winsB is 0.60, and wins both is 0.35. What is the probability that the candidate wins at least one office?
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