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7. (4 points) What is the probability that an integer from 1 to 1000, inclusive, chosen at random, is a multiple of 3 or a multiple of 7? 8. Eight people, including Joe and Ellen, are going to the movies and will sit in a row of 8 chairs. (a) (3 points) In how many ways can the eight people seat themselves? (b) (4 points) In how many ways can they seat themselves if Joe and Ellen must sit together? Note: The order here could be Joe Ellen or Ellen Joe. (c) (2 points) If all eight people sit down randomly, what is the probability that Joe and Ellen are seated next to each other?

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7. Total number of multiples of 3 between tå 4000 1 1000] = 333. Tot no. of multiples of 7= 1000 = 142. There will be common multiples: No. of such common multiples = 11000 = 47. 21 - so So tot. no. of multiples of either 3 or 1333 + 142 - 47 = brobability = 428 = 0.428. 7 428. T o 1000