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Help with some statistics questions please!!?

41.You are dealt two cards successively (without replacement)from a shuffled deck of 52 playing cards. find the probability that the first card is a king and the second card is a queen. 42. Among the contestants in a competition are 49 women and 20 men. If 5 winners are randomly slected, what is the probability that they are all men? round to 5 decimal places. 43. A bin contains 78 light bulbs of which 9 are defective. If 3 light bulbs are randomly selected from the bin with replacement, find the probability that allthe bulbs selected are good ones. Round to the nearestthousandth. 44. A sample of 4 different calculators is randomly selected from a group containing 16 that are defective and 30 that have no defects. What is the probability that at least one of the calculators is defective? 45. A study conducted at a certain college shows that 55% of the schools graduates find a job in their chosen feild within a year after graduation. Find the probability that among 7 randomly selected graduates, at least one finds a job in his or her chosen field within a year of graduating? 47. the library is given 3 books as a gift. The books will be selected from a list of 16 titles. If each book selected must have a different title, how many possible selections are there? 48. 8 basketball players are to be selected to play in a special game. the players will be selected from a list of 27 players. If the players are randomly selected, what is the probability that the 8 tallest players will be selected? 50. There are 6 members on a board of directors. Of they mmust elect a chairperson, a secretary, and a treasuer, how many different slates of candidates are possible? Please show me how to slove these?? thanks so much

Public Comments

1. 41. There are 4 kings in the deck. This means that the probability of drawing a king is 4/52. There are also 4 queens in the deck, but only 51 cards left. So drawing a queen has probability 4/51. The probability of both happening is 4/52 x 4/51. 42. The probability of drawing 1 man is 20/69, the probability of drawing a second man is (19/68), ... So the probability of drawing 5 man is (20x19x18x17x16) / (69x68x67x66x65) 43. Probability that a bulb is good: 69/78. Because we put the bulb back this probability is the same for the next two. So combining gives us (69/78)^3 44. This is 1 - probability that they are all in working order. So 1 - (16x15x14x13)/(46x45x44x43) 45. Same procedure as before but now with replacement. 1 - (0.45^7) 47. This is a 'combination'. 16 choices for the first, 15 for the second, 14 for the third, divide by 3! to eliminate permutations of the same solutions: (16x15x14)/6 48. This again uses a 'combination'. There is 1 correct group (we don't care about order). There are C = 27x26x25x24x23x22x21x20/8x7x6x5x4x3x2x1 possible choices. So probability of picking the correct one is 1/C. 50. Here order is important: 6 choices for chair, 5 left for secretary, 4 left for treasurer ==> 6x5x4.