51. A college has 10 basketball players. A 5 member's team and a captain will be selected out of these 10 players. How many different selections can be made?
52. How many four letter distinct initials can be formed using the alphabets of English language such that the last of the four words is always a consonant?
53. What is the total number of ways in which Dishu can distribute 9 distinct gifts among his 8 distinct girlfriends such that each of them gets at least one gift?
54. How many number of times will the digit 7 be written when listing the integers from 1 to 1000?
55. In how many ways can 15 people be seated around two round tables with seating capacities of 7 and 8 people?
56. In how many ways can the letters of the word EDUCATION be rearranged so that the relative position of the vowels and consonants remain the same as in the word EDUCATION?
57. A team of 8 students goes on an excursion, in two cars, of which one can seat 5 and the other only 4. In how many ways can they travel?
58. A tea expert claims that he can easily find out whether milk or tea leaves were added first to water just by tasting the cup of tea. In order to check this claims 10 cups of tea are prepared, 5 in one way and 5 in other. Find the different possible ways of presenting these 10 cups to the expert.
59. A committee is to be formed comprising 7 members such that there is a simple majority of men and at least 1 woman. The shortlist consists of 9 men and 6 women. In how many ways can this committee be formed?
60. How many alphabets need to be there in a language if one were to make 1 million distinct 3 digit initials using the alphabets of the language?
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