Permutations and Combinations
1. In how many different ways can the letters of the word ‘OFFICES’ be arranged?
(1) 2520
(2) 5040
(3) 1850
(4) 1680
(5) None of these
2. In how many different ways can the letters of the word “TRUST” be arranged?
(1) 60
(2) 240
(3) 120
(4) 25
(5) None of these
3. In how many different ways can 4 boys and 3 girls be arranged in a row such that all the boys stand together and all the girls stand together?
(1) 75
(2) 576
(3) 288
(4) 24
(5) None of these
Directions (Q. Nos. 4 to 5) Study the following information carefully to answer the questions that follow.
4. The committee should consist of 2 professors, 2 teachers and 1 reader?
(1) 450
(2) 225
(3) 55
(4) 90
(5) None of these
5. The committee should include all the 3 readers ?
(1) 90
(2) 180
(3) 21
(4) 55
(5) None of these
6. In how many different ways can the letters of the word TOTAL be arranged?
(1) 120
(2) 60
(3) 48
(4) 72
(5) None of these
7. Out of 5 men and 3 women, a committee of 3 members is to be formed so that it has 1 woman and 2 men. In how many different ways can this be done?
(1) 20
(2) 10
(3) 23
(4) 30
(5) None of these
8. In how many different ways can the letters of the word ‘FINANCE’ be arranged?
(1) 5040
(2) 2040
(3) 2510
(4) 4080
(5) None of these
9. In how many different ways can the letters of the word “SMART” be arranged?
(1) 25
(2) 60
(3) 180
(4) 200
(5) None of these
10. In how many different ways can the letters of the word ‘OPERATE’ be arranged?
(1) 5040
(2) 720
(3) 2520
(4) 360
(5) None of these
11. In how many different ways can the letters of the word ‘DAILY’ be arranged?
(1) 60
(2) 48
(3) 160
(4) 120
(5) None of these
12. In how many different ways can the lett3ers of the word ‘BLOATING’ be arranged?
(1) 40320
(2) 5040
(3) 2520
(4) 20160
(5) None of these
13. In how many different ways can the letters of the word ‘WEDDING’ be arranged?
(1) 5040
(2) 2500
(3) 2520
(4) 5000
(5) None of these
14. In how many different ways can the letters of the word ‘FLEECED’ be arranged?
(1) 840
(2) 2520
(3) 1680
(4) 49
(5) None of these
15. How many seven-digit numbers can be made from the number 3428651, using each digit only once?
(1) 49
(2) 180
(3) 5040
(4) 2520
(5) None of these
16. In how many different ways can 6 children be seated on 6 seats?
(1) 360
(2) 120
(3) 590
(4) 740
(5) None of these
17. In how many different ways can the letters of the word ‘PROBE’ be arranged?
(1) 15
(2) 25
(3) 60
(4) 125
(5) None of these
18. In how many ways can a committee of 4 people be choosen out of 8 people?
(1) 110
(2) 32
(3) 70
(4) 126
(5) None of these
19. In how many ways can 6 people be seated on a sofa if there are only 3 seats available?
(1) 18
(2) 120
(3) 2
(4) 216
(5) None of these
20. In how many different ways can the letters of the word ‘PRIDE’ be arranged?
(1) 60
(2) 120
(3) 15
(4) 360
(5) None of these
Directions (Q. Nos. 21 to 24) From the following, different committee are to be made as per the requirement given in each question.
In how many different ways can it be done? 10 men and 8 women out of which 5 men are teachers, 3 men are doctors and 2 are business men. Among th3e women, 3 are teachers, 2 are doctors, 2 are researchers and 1 is social worker.
21. A committee of 5 in the which 3 men and 2 women are there.
(1) 3360
(2) 8568
(3) 4284
(4) 1680
(5) None of these
22. A committee of 5 in which 2 men teachers, 2 women teachers and 1 doctor are there.
(1) 75
(2) 150
(3) 214
(4) 20
(5) None of these
23. A committee of 7.
(1) 31824
(2) 1200
(3) 9600
(4) 15912
(5) None of these
24. A committee of 3 in which there is no teacher and no doctor.
(1) 100
(2) 120
(3) 10
(4) 12
(5) None of these
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