Q. Let M be a sequence of 9 distinct integers sorted in ascending order. How many distinct pairs of sequences, N and O are there such that i) each are sorted in ascending order, ii) N has 5 and O has 4 elements, and iii) the result of merging N and O gives that sequence?

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Q. 14 different letters of alphabet are given, words with 6 letters are formed from these given letters. How many number of words are there which have at least one letter repeated?

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Q. In how many ways can 10 boys be seated in a row having 28 seats such that no two friends occupy adjacent seats?

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Q. How many ways can 8 prizes be given away to 7 students, if each student is eligible for all the prizes?

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Q. In a playground, 3 sisters and 8 other girls are playing together. In a particular game, how many ways can all the girls be seated in a circular order so that the three sisters are not seated together?

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Q. How many numbers of three digits can be formed with digits 1, 3, 5, 7 and 9?

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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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