BANK & INSURANCE (PERMUTATION AND COMBINATION) PART 2

Total Questions: 30

21. In a group of 7 boys and 9 girls, 5 members are to be selected. In how many different ways can they be selected such that at least one boy should be there?

Correct Answer: (b) 4242  
Solution:

Required number of ways
=> (7C4 and 9C1) or (7C3 and 9C2) or (7C2 and 9C3) or (7C1 and 9C4) or 7C5

=> (35 × 9) + (35 × 36) + (21 × 84) + (7 × 126) + 21
=> 315 + 1260 + 1764 + 882 + 21 = 4242

22. 17 buses are running between two places Nagercoil and Madurai. In how many ways can a family go from Nagercoil to Madurai and return by a different bus?

Correct Answer: (d) 272 ways
Solution:

They can go in any bus out of the total 17 buses.
They return by different buses, hence they cannot comeback in the same bus. Hence they can return in 16 ways.
Total number of ways = 17 × 16 = 272 ways

23. In a party hall, 10 persons are to be arranged around a round table. If two particular persons are not to be seated side by side, then what is the total number of arrangements?

Correct Answer: (b) 7 × 8!
Solution:

No. of ways to arrange 10 persons around the table
= (10 − 1)! = 9!
No. of ways in which 2 particular persons sit side by side = 8! × 2!
Therefore, required no. of arrangements = 9! − (8! × 2!)
= 9 × 8! − 8! × 2 × 1
= (9 − 2) × 8! = 7 × 8!

24. When 3 fair dice are rolled simultaneously, in how many outcomes will at least one of the dice show 3?

Correct Answer: (a) 91  
Solution:

When 3 dice rolled
=> Number of outcomes = 6³ = 216
Number of outcomes in which none of the 3 dice show 3 = 5³ = 125
Required no. of outcomes = 216 − 125 = 91

25. In a group of 6 girls and 5 boys, 3 members are to be selected. In how many different ways can they be selected such that at least one girl should be there?

Correct Answer: (c) 155
Solution:

The possibilities are,
=> (1 girl and 2 boys) or (2 girls and 1 boy) or (3 girls)

Required number of ways
=> (⁶C₁ and ⁵C₂) + (⁶C₂ and ⁵C₁) + (⁶C₃)
=> [6 × (5 × 4)/(1 × 2)] + [(6 × 5)/(1 × 2)] × 5] + [(6 × 5 × 4)/(1 × 2 × 3)]
=> 60 + 75 + 20 = 155

26. A teacher wants to select a boy out of 8 boys and a girl out of 7 girls for the writing competition. In how many ways can be select?

Correct Answer: (d) 56  
Solution:

Select a boy out of 8 boys and a girl out of 7 girls
= 8 × 7
Total ways = 56

27. In how many different ways a group of 5 men and 7 women can be formed out of 8 men and 10 women?

Correct Answer: (c) 6720
Solution:

Required number of ways
=> ⁸C₅ and ¹⁰C₇
=> [(8 × 7 × 6 × 5 × 4)/(5 × 4 × 3 × 2 × 1)] × [(10 × 9 × 8 × 7 × 6 × 5 × 4)/(7 × 6 × 5 × 4 × 3 × 2 × 1)]
=> 56 × 120 = 6720

28. In a bag contains 2 orange and 3 apples. If 2 fruits are selected, in how many ways that can be selected such that at least one is apple?

Correct Answer: (b) 9  
Solution:

 Required ways = ⁵C₂ − ²C₂ = 10 − 1 = 9

29. The bank manager forms a secret 2 – digit code from the numbers 0-9. But he set code as the first digit will not be 0 and the second number will not be even number. Then what are the possible ways to set the code?

Correct Answer: (d) 45  
Solution:First number will not be zero implies there are 9 possible way for digit one = ⁹C₁
And for second digit we have 5 possibilities = (1, 3, 5, 7, 9) = ⁵C₁
So the possible number of ways = 9 × 5 = 45

30. How many words can be formed by using all the letters of the word “NISARGA” so that the vowels are never together?

Correct Answer: (c) 2460  
Solution:

Required number of ways = (7!/2!) − (5! 3!/2!)
= [(7 × 6 × 5 × 4 × 3 × 2 × 1)/(2 × 1)]
− [(5 × 4 × 3 × 2 × 1)/(2 × 1)]
= 2460