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- FROM a group of 6 students A, B,C,D,E AND F , 3 are to be selected in the school commitee find the prob that A and B are not in the school committeeeFour rings are drawn from a box at a time and are not replaced.Determinewhetherthefollowingsequencestendtoinfinityandgiveafullargument establishing your claim (a)an= n/600 - 600/n (b) bn = n^n + (−n)^n (c) cn = 2^(n+2) + (−2)^(n−2)
- Show that A × B ≠ B × A, when A and B are nonempty,unless A = BIn drawing 3 CD’s from a lot, defective and non defective CD’s , let A, B , C and D mean at least one Defective CD, at least one non defective CD, 2 defective CD’s and 2 non defective CD’s, respectively. Are A and B mutually exclusive? Are C and D mutually exclusive? Comment on your results.Which condition would prove ΔDEF ∼ ΔJKL?
- In a group of 200 college students, 138 are enrolledin a course in psychology, 115 are enrolled in a course insociology, and 91 are enrolled in both. How many of thesestudents are not enrolled in either course? (Hint: Draw asuitable Venn diagram and fill in the numbers associatedwith the various regions.)Suppose that in a particular class of 200 students, 31 of them plan on majoring in math, 27 plan onmajoring in history, and 18 plan on double majoring in math and history. How many want to major inexactly one of psychology or math? (Hint: Look at the Venn diagram and figure out which regionscorrespond to “exactly one”; do not try and write the set down!)Let A be the set of positive integers that are less than or equal to 40 and are multiples of 4 and let B be the set of positive integers that are less than or equal to 40 and are multiples of 6. Determine the number of elements in AUB?
- Ifn(A)=5,n(B)=11and? ?∩? =3,whatis? ?∪? ?A committee of 5 delegates is to be chosen from a group of 17 delgates, 10 ofwhom are women. If at most 3 of the delegates in the committee are to bewomen, what is the total number of distinct committees which can be chosen?A California study concluded that following 7simple health rules can extend a man’s life by 11 yearson the average and a woman’s life by 7 years. These7 rules are as follows: no smoking, get regular exer-cise, use alcohol only in mo deration, get 7 to 8 hoursof sleep, maintain prop er weight, eat breakfast, and do not eat between meals. In how many ways can a personadopt 5 of these rules to follow(a) if the person presently violates all 7 rules?(b) If the person never eats between meals and always exercises daily?