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Permutation Combination, Probability Questionbank

Permutation combination and probability is a frequently tested topic in the Quant section of CAT

This is one of the favourite topics with CAT Question setters, and one can expect anything from one to five questions from these two topics. Here is a list of sample questions on this topic.m

1. Question 1  How many five digit positive integers that are divisible by 3 can be formed using the digits 0, 1, 2, 3, 4 and 5, without any of the digits getting repeated in a number?
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2. Question 2  In how many ways can 5 different toys be packed in 3 identical boxes such that no box is empty, if any of the boxes may hold all of the toys?
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3. Question 3  There are 2 brothers among a group of 20 persons. In how many ways can the group be arranged around a circle so that there is exactly one person between the two brothers?
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4. Question 4  In how many ways can 15 people be seated around two round tables with seating capacities of 7 and 8 people?
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5. Question 5: In how many ways can the letters of the word ABACUS be rearranged such that the vowels always appear together?
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6. Question 6: There are 6 boxes numbered 1, 2,...6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is
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