IOE Preparation Questions of Permutation & Combination

Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?

In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?

From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there in the committee. In how many ways can it be done?

In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?

In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together?

In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?

In how many different ways can the letters of the word 'MATHEMATICS' be arranged such that the vowels must always come together?

There are 8 men and 10 women and you need to form a committee of 5 men and 6 women. In how many ways can the committee be formed?

How many 3-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed?

In how many different ways can the letters of the word 'LEADING' be arranged such that the vowels should always come together?

A coin is tossed 3 times. Find out the number of possible outcomes.

In how many different ways can the letters of the word 'DETAIL' be arranged such that the vowels must occupy only the odd positions?

A bag contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the bag, if at least one black ball is to be included in the draw?

In how many different ways can the letters of the word 'JUDGE' be arranged such that the vowels always come together?

In how many ways can the letters of the word 'LEADER' be arranged?

How many words can be formed by using all letters of the word 'BIHAR'?

How many arrangements can be made out of the letters of the word 'ENGINEERING' ?

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

How many words with or without meaning, can be formed by using all the letters of the word, 'DELHI' using each letter exactly once?

What is the value of 100P2 ?

In how many different ways can the letters of the word 'RUMOUR' be arranged?

There are 6 periods in each working day of a school. In how many ways can one organize 5 subjects such that each subject is allowed at least one period?

How many 6 digit telephone numbers can be formed if each number starts with 35 and no digit appears more than once?

An event manager has ten patterns of chairs and eight patterns of tables. In how many ways can he make a pair of table and chair?

25 buses are running between two places P and Q. In how many ways can a person go from P to Q and return by a different bus?

A box contains 4 red, 3 white and 2 blue balls. Three balls are drawn at random. Find out the number of ways of selecting the balls of different colours?

A question paper has two parts P and Q, each containing 10 questions. If a student needs to choose 8 from part P and 4 from part Q, in how many ways can he do that?

In how many different ways can 5 girls and 5 boys form a circle such that the boys and the girls alternate?

Find out the number of ways in which 6 rings of different types can be worn in 3 fingers?

In how many ways can 5 man draw water from 5 taps if no tap can be used more than once?

How many two digit numbers can be generated using the digits 1,2,3,4 without repeating any digit?

There are three places P, Q and R such that 3 roads connects P and Q and 4 roads connects Q and R. In how many ways can one travel from P to R?

There are 10 women and 15 men in an office. In how many ways can a person can be selected?

There are 10 women and 15 men in an office. In how many ways a team of a man and a woman can be selected?

In how many ways can three boys can be seated on five chairs?

There are 6 persons in an office. A group consisting of 3 persons has to be formed. In how many ways can the group be formed?

There are 5 yellow, 4 green and 3 black balls in a bag. All the 12 balls are drawn one by one and arranged in a row. Find out the number of different arrangements possible.

In how many ways can 7 boys be seated in a circular order?

In how many ways can 7 beads can be arranged to form a necklace?

In how many ways can a team of 5 persons be formed out of a total of 10 persons such that two particular persons should be included in each team?

In how many ways can a team of 5 persons be formed out of a total of 10 persons such that two particular persons should not be included in any team?

How many triangles can be formed by joining the vertices of an octagon?

If there are 9 horizontal lines and 9 vertical lines in a chess board, how many rectangles can be formed in the chess board?

Find the number of diagonals of a decagon?

Find the number of triangles that can be formed using 14 points in a plane such that 4 points are collinear?

What is the sum of all 4 digit numbers formed using the digits 2, 3,4 and 5 without repetition?

In a birthday party, every person shakes hand with every other person. If there was a total of 28 handshakes in the party, how many persons were present in the party?

There are 8 points in a plane out of which 3 are collinear. How many straight lines can be formed by joining them?

How many quadrilaterals can be formed by joining the vertices of an octagon?

How many straight lines can be formed by joining 12 points on a plane out of which no points are collinear?