Q. When four coins are tossed simultaneously, in _______ number of the outcomes at most two of the coins will turn up as heads.

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Q. How many numbers must be selected from the set {1, 2, 3, 4} to guarantee that at least one pair of these numbers add up to 7?

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Q. During a month with 30 days, a cricket team plays at least one game a day, but no more than 45 games. There must be a period of some number of consecutive days during which the team must play exactly ______ number of games.

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Q. In how many ways can 8 different dolls be packed in 5 identical gift boxes such that no box is empty if any of the boxes hold all of the toys?

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Q. A group of 20 girls plucked a total of 200 oranges. How many oranges can be plucked one of them?

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Q. In a get-together party, every person present shakes the hand of every other person. If there were 90 handshakes in all, how many persons were present at the party?

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Q. A bag contains 25 balls such as 10 balls are red, 7 are white and 8 are blue. What is the minimum number of balls that must be picked up from the bag blindfolded (without replacing any of it) to be assured of picking at least one ball of each colour?

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Q. How many substrings (of all lengths inclusive) can be formed from a character string of length 8? (Assume all characters to be distinct)

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Q. The number of diagonals can be drawn in a hexagon is ______

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Q. The number of binary strings of 17 zeros and 8 ones in which no two ones are adjacent is ___________

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Q. How many words that can be formed with the letters of the word ‘SWIMMING’ such that the vowels do not come together? Assume that words are of with or without meaning.

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Q. A number lock contains 6 digits. How many different zip codes can be made with the digits 0–9 if repetition of the digits is allowed upto 3 digits from the beginning and the first digit is not 0?

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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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