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Five persons A, B, C, D and E are in queue of a shop. The Probability that A and B are always together is

Options

  1. A2 5
  2. B1 4
  3. C3 5
  4. D2 3

Correct answer

A. 2 5

Step-by-step solution

The total number of ways to arrange 5 persons A, B, C, D, E in a queue is 5! = 120 . To find the number of arrangements where A and B are always together, treat (AB) as a single unit. Now, we have 4 units: (AB), C, D, E . These 4 units can be arranged in 4! = 24 ways. Within the unit (AB) , A and B can be arranged in 2! = 2 ways ( AB or BA ). Therefore, the total number of favorable arrangements is 24 2 = 48 . The probability is the ratio of favorable arrangements to total arrangements: P = 48 120 = 2 5 . Answer: 2

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