Q. The size of a multiset is 6 which is equal to the number of elements in it with counting repetitions (a multiset is an unordered collection of elements where the elements may repeat any number of times). Determine the number of multisets can be grouped from n distinct elements so that at least one element occurs exactly twice?

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Q. How many words can be formed with the letters of the word ‘CASTLE’ when ‘O’ and ‘A’ occupying end places.

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Q. Determine the number of ways of choosing a cricket team (consists of 11 players) out of 18 players if a particular player is never chosen.

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Q. How many different choices can be made from 5 roses, 4 marigold and 8 sunflowers if at least one flower is to be chosen for making of garland?

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Q. In how many ways 6 pens can be selected from 15 identical black pens?

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Q. Determine the number of ways of selecting one or more letters from the letters BBBBBB?

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Q. Determine the number of ways such that 5 men and 5 women be seated at a round table if no two women are seated together.

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Q. Find the number of ways in which 4 people E, F, G, H, A, C can be seated at a round table, such that E and F must always sit together.

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Q. There are 6 equally spaced points A, B, C, D, E and F marked on a circle with radius R. How many convex heptagons of distinctly different areas can be drawn using these points as vertices?

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Q. There are 2 twin sisters among a group of 15 persons. In how many ways can the group be arranged around a circle so that there is exactly one person between the two sisters?

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Q. The number of words of 4 consonants and 3 vowels can be made from 15 consonants and 5 vowels, if all the letters are different is ________

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Q. How many ways are there to arrange 7 chocolate biscuits and 12 cheesecake biscuits into a row of 19 biscuits?

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Q. If a, b, c, d and e are five natural numbers, then find the number of ordered sets(a, b, c, d, e) possible such that a+b+c+d+e=75.

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Q. There are 15 people in a committee. How many ways are there to group these 15 people into 3, 5, and 4?

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Q. There are six movie parts numbered from 1 to 6. Find the number of ways in which they be arranged so that part-1 and part-3 are never together.

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Q. How many ways are there to divide 4 Indian countries and 4 China countries into 4 groups of 2 each such that at least one group must have only Indian countries?

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Q. Find the number of factors of the product 5⁸ * 7⁵ * 2³ which are perfect squares.

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Q. From a group of 8 men and 6 women, five persons are to be selected to form a committee so that at least 3 women are there on the committee. In how many ways can it be done?

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Q. Calculate sum of divisors of n = 1900.

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Q. Given the factorization of a number n, then the sum of divisors can be computed in _______

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