61. How many arrangements of four 0's (zeroes), two 1's and two 2's are there in which the first 1 occur before the first 2?
62. How many different five-letter words can be formed using the letter from the world APPLE?
63. I have an amount of Rs. 10 lakh, which I went to invest in stocks of some companies. I always invest only amounts that are multiples of Rs 1 lakh in the stock of any company. If I can choose from among the stocks of five different companies, In how many ways can I invest the entire amount that I have?
64. A selection committee is to be chosen consisting of 5 ex-technicians. Now there are 12 representatives from four zones. It has further been decided that if Mr. X is selected, Y and Z will not be selected and vice-versa. In how many ways it can be done?
65. How many 5-digit positive integers exist the sum of whose digits are odd?
66. There are eight boxes of chocolates, each box containing distinct number of chocolates from 1 to 8. In how many ways four of these boxes can be given to four persons (one boxes to each) such that the first person gets more chocolates than each of the three, the second person gets more chocolates than the third as well as the fourth persons and the third person gets more chocolates than fourth person?
67. In how many ways can seven friends be seated in a row having 35 seats, such that no two friends occupy adjacent seats?
68. How many ways can 10 letters be posted in 5 post boxes, if each of the post boxes can take more than 10 letters?
69. In a hockey championship, there are 153 matches played. Every two team played one match with each other. The number of teams participating in the championship is:
70. A box contains 10 balls out of which 3 are red and rest are blue. In how many ways can a random sample of 6 balls be drawn from the bag so that at the most 2 red balls are included in the sample and no sample has all the 6 balls of the same colour?
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