81. A local delivery company has three packages to deliver to three different homes. if the packages are delivered at random to the three houses, how many ways are there for at least one house to get the wrong package?
82. How many natural numbers less than a lakh can be formed with the digits 0,6 and 9?
83. There are 20 couples in a party. Every person greets every person except his or her spouse. People of the same sex shake hands and those of opposite sex greet each other with a Namaste (It means bringing one's own palms together and raising them to the chest level). What is the total number of handshakes and Namaste's in the party?
84. In how many ways can a leap year have 53 Sundays?
85. In a certain laboratory, chemicals are identified by a colour-coding system. There are 20 different chemicals. Each one is coded with either a single colour or a unique two-colour pair. If the order of colours in the pairs does not matter, what is the minimum number of different colours needed to code all 20 chemicals with either a single colour or a unique pair of colours?
86. Six boxes are numbered 1, 2, 3, 4, 5 and 6. Each box must contain either a white ball or a black ball. At least one box must contain a black ball and boxes containing black balls must be consecutively numbered. find the total number of ways of placing the balls.
87. In how many ways can 6 green toys and 6 red toys be arranged, such that 2 particular red toys are never together whereas 2 particular green toys are always together?
88. There are five comics numbered from 1 to 5. In how many ways can they be arranged, so that part-1 and part-3 are never together?
89. The number of ways which a mixed double tennis game can be arranged amongst 9 married couples if no husband and wife play in the same is:
90. Ten coins are tossed simultaneously. In how many of the outcomes will the third coin turn up a head?
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