Determine the quantity of different signals that can be created by organizing at least 2 flags in sequence (one below the other) on a vertical staff, if 5 different flags are available?

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AAI ATC Junior Executive 25 March 2021 Official Paper (Shift 1)
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  1. 120
  2. 320
  3. 420
  4. 440

Answer (Detailed Solution Below)

Option 2 : 320
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Detailed Solution

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Given:

Available flags = 5

Sequence matters

Concept:

Ways of arranging r things out of n distinct things = 

Formula:

 = 

Explanation:

At least two flags from 5 flags mean ' 2 flags or 3 flags or 4 flags or 5 flags '.

∴ ways =  +  +  + 

= (4)(5) + (3)(4)(5) + (2)(3)(4)(5) + (1)(2)(3)(4)(5)

= 20 + 60 + 120 + 120

= 320

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