One red flower, three white flowers, and two blue flowers are arranged in a line such that
I. No two adjacent flowers are of the same color.
II. The flowers at the two ends of the line are of different colors.
In how many different ways can the flowers be arranged?
2
4
6
10
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1
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The students in a class are seated, according to their marks in the previous examination. Once, it so happens that four of the students got equal marks and therefore the same rank. To decide their seating arrangement, the teacher wants to write down all possible arrangements one in each of separate bits of paper in order to choose one of these by lots. How many bits of paper are required?
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10
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How many natural numbers can be made with digits 0, 7, 8 which are greater than 0 and less than a million?
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2
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A fair coin is tossed 5 times. What is the probability of getting at least three heads on consecutive tosses?
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3
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A committee of 8 members is to be selected from a group of 12 male and 10 female members. In how many ways the committee is selected such that at most two and at least one male member are there in the committee?
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4
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There are 6 letters for 3 envelopes. In how many different ways can the envelopes be filled?
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5
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Four letters are selected from the word “CAPAME” and are rearranged to form four letter words. How many words can be formed?
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6
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A teacher has to choose the maximum different groups of three students from a total of six students. Of these groups, in how many groups there will be included in a particular student?
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7
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A five-letter word is to be formed from a group of 5 vowels and 4 consonants, using at least one vowel and at least one consonant. In how many ways the word having a greater number of consonants than vowels can be formed?
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8
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How many words, with or without meaning, can be formed using all letters of the word EQUATION using each letter exactly once?
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9
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Find the probability that a leap year selected at random will contain 53 Sundays
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