Find the probability that a leap year selected at random will contain 53 Sundays
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1
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If C(n, 7) = C(n, 5), find n
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10
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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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2
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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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3
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Seven different objects must be divided among three people. In how many ways can this be done if one or two of them must get no objects?
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4
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In how many ways a committee, consisting of 5 men and 6 women can be formed from 8 men and 10 women?
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5
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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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6
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If a team of 4 persons is to be selected from 8 males and 8 females, then in how many ways can the selections be made to include at least 1 female
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7
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Six boys and 4 girls are to be seated in two separate rows with five chairs each, such that two particular girls are always together and all the girls are not in the same row. In how many ways can they be seated?
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8
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Ten participants are participating in a competition. In how many ways can the first three prizes be won?
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9
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One card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is not a face card (Jack, Queen and King only)?
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