# Practice Questions on Permutation-CombinationAptitude Questions and Answers

## Difficult Permutation-Combination Question - 1

 Q1. The number of ways of arranging $n$ students in a row such that no two boys sit together and no two girls sit together is $m(m > 100)$. If one more student is added, then number of ways of arranging as above increases by $200\%$, The value of $n$ is:
 A. $12$ B. $8$ C. $9$ D. $10$

## Difficult Permutation-Combination Question - 2

 Q2. How many integers, greater than 999 but not greater than 4000, can be formed with the digits 0, 1, 2, 3 and 4, if repetition of digits is allowed?
 A. 499 B. 500 C. 375 D. 376 E. 501

## Difficult Permutation-Combination Question - 3

 Q3. 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 repeating?
 A. 15 B. 96 C. 216 D. 120 E. 625

## Difficult Permutation-Combination Question - 4

 Q4. There are 10 seats around a circular table. If 8 men and 2 women have to seated around a circular table, such that no two women have to be separated by at least one man. If $P$ and $Q$ denote the respective number of ways of seating these people around a table when seats are numbered and unnumbered, then $P : Q$ equals,
 A. $9 : 1$ B. $72 : 1$ C. $10 : 1$ D. $8 : 1$

## Difficult Permutation-Combination Question - 5

 Q5. How many factors of $2^5 × 3^6 × 5^2$ are perfect squares?
 A. $20$ B. $24$ C. $30$ D. $36$
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