21. From a group of seven men and six women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done? |
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22. In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together? |
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23. In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together? |
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24. In how many different ways can five girls and five boys form a circle such that the boys and the girls alternate? |
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25. A question paper has 2 parts P and Q, each containing ten questions. If a student needs to choose 8 from part P and 4 from part Q, in how many ways can he do that? |
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26. A box contains four red, three white and two blue balls. Three balls are drawn at random. Find out the number of ways of selecting the balls of different colours? |
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27. 25 Cars are running between two places P and Q. In how many ways can a person go from P to Q and return by a different car? |
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28. An event manager has 10 patterns of chairs and 8 patterns of tables. In how many ways can he make a pair of table and chair? |
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29. There are 6 periods in each working day of a school. In how many ways can one arrange 5 subjects such that each subject is allowed at least one period? |
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30. What is the value of 100P2 ? |
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Those are all planning for any competitive examinations can use this segment to enhance their abilities.