BANK & INSURANCE (PERMUTATION AND COMBINATION) PART 1

Total Questions: 30

11. In how many different ways can the letters of the word “CABINET” be arranged?

Correct Answer: (a) 5040  
Solution:Required ways = 7! = 5040

12. A teacher and head master are chosen out of a group having 15 persons. How many ways are there?

Correct Answer: (d) 240  
Solution:

Total number of ways = 15 × 14 = 210

13. In how many ways the letters of the word ‘ARMOUR’ can be arranged?

Correct Answer: (b) 360  
Solution:Total letters = 6, but R has come twice.
No of arrangements = 6!/2! = (6 × 5 × 4 × 3 × 2 × 1)/(2 × 1) = 360

14. How many four letter words can be formed out of the letters of the word is “LOGARITHMS”?

Correct Answer: (c) 5040
Solution:

Number of letters = 10!/(10 − 4)!
= 720 × 7 = 5040

15. In how many ways word “BANKING” can be arranged in such a way that all vowels and consonants comes together?

Correct Answer: (d) 240  
Solution:

Vowels = A, I = 2!
Consonant = B, N, K, N, G = 5!
Required ways = 2! × 5!/2! × 2! = 240

16. In a class has 3 boys and 2 girls, two students were selected. In how many different ways can they be selected such that at least one girl should be there?

Correct Answer: (c) 7
Solution:

Total number of ways = ⁵C₂
No girls selected = ³C₂
Required ways = ⁵C₂ − ³C₂ = 10 − 3 = 7

17. Two students are selected from 8 students. How many ways are there to achieve this?

Correct Answer: (c) 56
Solution:

Number of ways = 8 × 7 = 56

18. In how many ways the letters of the word “COURSE” can be arranged?

Correct Answer: (e) None of these
Solution:

Required ways = 6! = 720

19. A bag contains 4 red balls and three green balls. If two balls are selected, in how many different ways the balls selected such that at least one red ball should be there?

Correct Answer: (a) 18  
Solution:

Total number of ways = ⁷C₂
No red balls = ³C₂
Required ways = ⁷C₂ − ³C₂
= 7 × 6/2 − 3 × 2/2
= 36/2 = 18

20. How many three digit numbers can be formed with the digits 2, 3, 5, 6, 9, if repetition of digits is allowed?

Correct Answer: (e) None of these
Solution:

The number of ways in three digit no’s can be formed from the given digit is 5 × 5 × 5
= 125