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Doctors Medicines MCQs Q&A

  1. Quantity A > Quantity B
  2. Quantity A < Quantity B
  3. Quantity A ≥ Quantity B
  4. Quantity A ≤ Quantity B
  5. Quantity A = Quantity B or no relation
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1 Answers

Option 2 : Quantity A < Quantity B

Quantity A:

⇒ Number of vacancies = 6

Given, number of applications received from males = number of vacancies

⇒ Number of applications received from males = 6

Also, number of applications received from males and females are equal,

⇒ Number of applications received from females = 6

Now according to the condition, at least four females must be selected, so three cases are possible

1. Selection of 4 females and 2 males

2. Selection of 5 females and 1 male

3. Selection of all 6 females

⇒ Number of ways possible for first case = 6C4 × 6C2 = 15 × 15 = 225

⇒ Number of ways possible for second case = 6C5 × 6C1 = 6 × 6 = 36

⇒ Number of ways possible for third case = 6C6 = 1

⇒ Total possible cases = 225 + 36 + 1 = 262

⇒ Quantity A = 262

Quantity B:

⇒ Total number of socks = 4 pairs = 8 socks

Now, first socks can be chosen in 8 ways.

Now, 7 socks are remaining and since no pair of socks can be completed, hence second socks can be selected from 6 socks only, excluding the one which is similar to first drawn socks,

⇒ Number of ways of selecting second socks = 6

Now, 6 socks are remaining, but to fulfil the condition, the third socks can be selected from only 4 socks,

⇒ Number of ways in which third socks can be drawn = 4

Now, 5 socks are remaining, and 3 socks are similar to the socks that has been taken out, so to fulfil the condition, the fourth socks can be taken out from remaining 2 socks only

⇒ Number of ways of selecting fourth socks = 2

⇒ Total number of ways of selecting 4 socks = 8 × 6 × 4 × 2 = 384

⇒ Quantity B = 384

∴ Quantity A < Quantity B
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