Permutations & Combinations Questions with Solutions

There are 8 students appearing in an examination of which 3 have to appear in Mathematics paper and the remaining 5 in different subjects. Then, the number of ways they can be made to sit in a row, if the candidates in Mathematics cannot sit next to each other is

How many even integers between 4000 and 7000 have four different digits?

The number of bit strings of length 8 that start with the bit 0 or end with the bits 11 is

If $42\cdot {}^n{P}_2={}^n{P}_4$, then the value of $n$ is

The number of bit strings of length 10 that contain either five consecutive 0's or five consecutive 1's is

How many 3-digit numbers divisible by 5 can be formed using the digits 2, 3, 5, 6, 7 and 9, without repetition of digits?

Let A and B be two sets containing four and two elements respectively. The number of subsets of A × B, each having at least three elements, is

From a group of 7 men and 6 women, a committee of 5 persons with more males than females is to be formed. In how many ways can this be done?

9 balls are to be placed in 9 boxes and 5 of the balls cannot fit into the 3 small boxes. The number of ways of arranging one ball in each of the boxes is

A student council has 10 members. From these, one President, one Vice-President, one Secretary, one Joint-Secretary and two Executive Committee members have to be elected. In how many ways can this be done?

How many natural numbers smaller than $2\times {10}^8$ can be formed using the digits 1 and 2 only?

Let n be the number of different 5-digit numbers, divisible by 4, that can be formed with the digits 1, 2, 3, 4, 5 and 6, with no digit being repeated. What is the value of n?

If all the words, with or without meaning, are written using the letters of the word QUEEN and are arranged as in an English dictionary, then the position of the word QUEEN is

In a chess tournament, n men and 2 women players participated. Each player plays 2 games against every other player. Also, the total number of games played by the men among themselves exceeded by 66 the number of games that the men played against the women. Then the total number of players in the tournament is

Ten points are marked on a straight line and eleven points are marked on another straight line. How many triangles can be constructed with vertices from among the above points?

How many 4-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9 which are divisible by 5, if none of the digits is repeated?

How many positive numbers less than 10,000 are such that the product of their digits is 210?

There are 9 bottles labelled 1, 2, 3, ..., 9 and 9 boxes labelled 1, 2, 3, ..., 9. The number of ways one can put these bottles in the boxes so that each box gets one bottle and exactly 5 bottles go in their corresponding numbered boxes is

The value of ${\sum }_{r=1}^n\frac{{}^n{P}_r}{r!}$ is

Lines $L_1,L_2,\dots ,L_{10}$ are distinct, among which the lines $L_2,L_4,L_6,L_8,L_{10}$ are parallel to each other and the lines $L_1,L_3,L_5,L_7,L_9$ pass through a given point C. The number of points of intersection of pairs of lines from the complete set $L_1,L_2,\dots ,L_{10}$ is