Q. There are two different Geography books, five different Natural Sciences books, three different History books and four different Mathematics books on a shelf. In how many different ways can they be arranged if all the books of the same subjects stand together?

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Q. The code for a safe is of the form PPPQQQQ where P is any number from 0 to 9 and Q represents the letters of the alphabet. How many codes are possible for each of the following cases? Note that the digits and letters of the alphabet can be repeated.

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Q. Amit must choose a seven-digit PIN number and each digit can be chosen from 0 to 9. How many different possible PIN numbers can Amit choose?

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Q. A head boy, two deputy head boys, a head girl and 3 deputy head girls must be chosen out of a student council consisting of 14 girls and 16 boys. In how many ways can they are chosen?

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Q. A drawer contains 12 red and 12 blue socks, all unmatched. A person takes socks out at random in the dark. How many socks must he take out to be sure that he has at least two blue socks?

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Q. The least number of computers required to connect 10 computers to 5 routers to guarantee 5 computers can directly access 5 routers is ______

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Q. In a group of 267 people how many friends are there who have an identical number of friends in that group?

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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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