BANK & INSURANCE (PERMUTATION AND COMBINATION) PART 3

Total Questions: 30

11. Find the number of ways in which four couples can sit around a circular dining table such that no two females sit together?

Correct Answer: (c) 144
Solution:No. of ways to arrange 4 males in circular dining table = (4−1)! = 3!
Now, No. of ways to arrange 4 females = 4!
= 6 × 24 = 144

12. Find the ways to arrange the letters of word “ACHIEVEMENT” such that all vowels come together.

Correct Answer: (d) 1,00,800
Solution:Word ⇒ ACHIEVEMENT
Vowel ⇒ 5
Constant ⇒ 6
No. of ways = 7! × 5! / 3! ⇒ 100800

13. From a group of 5 men and 10 women a committee has to be formed of 5 members in which at least 2 men are required. Find the number of ways to form the committee.

Correct Answer: (a) 1701  
Solution:

No. of way = ⁵C₂ × ¹⁰C₃ + ⁵C₃ × ¹⁰C₂ + ⁵C₄ × ¹⁰C₁ + ⁵C₅
= 1200 + 450 + 50 + 1 = 1701

14. Find number of ways in which four digits number can be formed from digits 0, 2, 3, 4, 6, 5 without any repetition such that each number is divisible by 5?

Correct Answer: (c) 108
Solution:

5 × 4 × 3 × 1 + 4 × 4 × 3 × 1
Required ways = 60 + 48 = 108

15. 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)?

Correct Answer: (b) 210  
Solution:

Total required numbers between 2000 & 3000
= 210

16. In a bucket there are different coloured packets of black, blue and white colours. The probability of selecting one black packet out of the total packet is 2/5 and the probability of selecting one blue packet out of the total packet is 3/7. The number of white packet in the bag is 18. Find total number of packets in the bucket?

Correct Answer: (b) 105  
Solution:Let, total no. of packet in bucket be 35x,
Then no. of black packets = 2/5 × 35x = 14x
And no. of blue packets = 3/7 × 35x = 15x
Now, 14x + 15x + 18 = 35x
6x = 18
x = 3
Total no. of boxes = 35 × 3 = 105

17. In how many different ways can letter of the word “COMPLAINT” be arranged in such a way that vowels occupy only the odd positions?

Correct Answer: (b) 43200  
Solution:

Vowels in COMPLAINT = (O, A, I)
Ways to arrange vowels in odd position = ⁵P₃ × 6!
= 5 × 4 × 3 × 720 = 43200
Alternate method
Required Ways = ⁵C₃ × ⁶C₆ × 6! × 3!
= 43200

18. In jack & jones store, stock is available of three colour of t-shirts black, blue and red. Probability of selling one black t-shirt is 1/6, one blue t-shirt is 2/7. If in store number of red colour t-shirts are 207. Then find difference between stock available of total black t-shirts and blue t-shirts?

Correct Answer: (e) 45
Solution:

Let total stock available in store = 42x
Black T-shirt = 42x = 7x
Blue T-shirt = 42x × (2/7) = 12x
7x + 12x + 207 = 42x
∴ x = 207 / 23
x = 9
Required difference = 12x − 7x = 5x
= 5 × 9 = 45

19. In how many ways the letters of the word ‘GALAXY’ can be arranged such that G and Y are always at end places?

Correct Answer: (b) 24  
Solution:Required ways = (4! / 2!)*2!  = 24

20. In how many different ways can the letters of the word ‘FRANCE’ be arranged so that vowels do not come together?

Correct Answer: (c) 480
Solution:Total arrangement = 6! = 720
When vowels come together 5!2! = 240
Therefore, Total arrangement when vowels do not come together = 720 − 240 = 480