Permutations & Combinations

Q.

What are the collective nouns of books?

Q. From a group of 7 men and 6 women 5 people are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways an it be done?

1. 756
2. 735
3. 564
4. 645

Q. How many numbers between 2000 and 3000 can be formed with the digits 0, 1, 2, 3, 4, 5, 6, 7 (repetition of digits not allowed)?

1. 42
2. 210
3. 336
4. 440

Q.

Two families with three members each and one family with four members are to be seated in a row. In how many ways can they be seated so that the same family members are not separated?

1. $2!3!4!$

2. ${\left(3!\right)}^3\times 4!$

3. $3!\times {\left(4!\right)}^3$

4. ${\left(3!\right)}^2\times 4!$

Q. A three-member committee has to be formed from a group of 9 people. How many such distinct committees can be formed?

1. 27
2. 72
3. 81
4. 84

Q. In how many different ways, the letters of the word ALGEBRA can be arranged in a row if
(i) The two As are together ?
(ii) The two As are not together ?

1. (i) 720, (ii) 1800
2. (i) 620, (ii) 1600
3. (i) 780, (ii) 1860
4. (i) 720, (ii) 1600

Q. Five teams have to compete in a league, with every team playing every other team exactly once before going to the next round. How many matches will have to held to complete the league round of matches?

1. 20
2. 10
3. 8
4. 5

Q. In how many ways can a person send invitation cards to 6 of his friends if he has four servants to distribute the cards?

1. $6^4$
2. $4^6$
3. 24
4. None of these

Q. There are 3 Indians and 3 Chinese in a group of 6 people. How many subgroups of this group can we choose so that every subgroup has at least one Indian ?

1. $56$
2. $52$
3. $48$
4. $44$

Q. Below is a square grid of 8$\times$8


What is total No. of squares in the grid ?

1. 204
2. 285
3. 140
4. None of these

Q. In a hockey championship, there were 153 matches played. Every two teams played one match with each other. The number of teams participating in the championship is

1. 18
2. 19
3. 17
4. 16

Q. In how many ways can 7 Indians, 5 Pakistanis and 6 Dutch be seated in a row so that all persons of the same nationally sit together ?

1. 3!
2. 7!5!6!
3. 3!7!5!6!
4. 18!

Q. There are 15 people to be seated around a round table. In how many ways we can arrange them such that there is no restriction

1. 14!
2. 13!
3. 12!
4. 11!

Q. The letters of word PROMISE are arranged so that no two of the vowels should come together. Find the total number of arrangements.

1. 49
2. 1440
3. 7
4. 1898

Q. How many parallelograms will be formed if 7 parallel horizontal lines intersected by 6 parallel vertical lines?

1. 42
2. 294
3. 315
4. None of these

Q. A cricket team of 11 players is to be formed from 20 players including 6 bowlers and 3 wicket keepers. The number of ways in which a team can be formed having exactly 4 bowlers and 2 wicket keepers is

1. 20790
2. 6930
3. 10790
4. 360

Q. In how many ways can Ram choose a vowel and a consonant from the letter ALLAHABAD ?

1. 4
2. 6
3. 9
4. 5

Q.

What is phrasal verb? What is the phrasal verb of distributed?

Q. How many 7-digit numbers are there having the digit 3(three times ) and the digit 0(four times ) ?

1. 15
2. $3^3\times 4^4$
3. 30
4. None of these

Q. How many batting orders are possible for the Indian cricket team if there is a squad of 15 to choose from such that Sachin Tendulkar is always chosen ?

1. $1001\times 11!$
2. $364\times 11!$
3. 11!
4. $15\times 11!$

Q.

The number of circular permutations of $n$ different objects is?

1. $n!$

2. $n$

3. $\left(n-2\right)!$

4. $\left(n-1\right)!$

Q. In how many ways can the letters of the word EQUATION be arranged so that all the vowels come together ?

1. ${}^9{C}_4.{}^9{C}_5$
2. $4!\times 5!$
3. 9!/5!
4. 9! - 4!5!

Q. An e-mail password must contain three characters. The password has to contain one numeral from 0 to 9, one upper case and one lower case character from the English alphabet. How many distinct passwords are possible ?

1. 
   $6,760$
2. 
   $13,520$
3. 
   $40,560$
4. 
   $1,05.456$

Q. A captain and vice-captain are to be chosen out of a team having 11 players. How many ways are there to achieve this ?

1. $10\times 9$
2. ${}^{11}{C}_2$
3. 110
4. 109!

Q. There are 25 points on a plane of which 7 are collinear. How many straight lines can be formed ?

1. 7
2. 300
3. 280
4. None of these

Q. There are 15 people to be seated around a round table. In how many ways we can arrange them such that A, B, C all three are never together

1. $12!\times 3!$
2. $12!\times 176$
3. $12!\times 182$
4. $12!\times 142$

Q. A six sided unbiased die with four green faces and two red faces is rolled seven times. Which of the following combinations is the most likely outcome of the experiment?

1. 
   Three green faces and four red faces
2. 
   Four green faces and three red faces
3. 
   Five green faces and two red faces
4. 
   Six green faces and one red face

Q. There are 25 points on a plane of which 7 are collinear. How many triangles can be formed from these points ?

1. 453
2. 2265
3. 755
4. None of these

Q. In how many ways can the letters of the word PATNA be rearranged ?

1. 60
2. 120
3. 119
4. 59

Q. Seven points lie on a circle. How many chords can be drawn by joining these points.

1. 22
2. 21
3. 23
4. 24