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Counting and Basic Probability · Question 27 of 65

Question 27

MediumOriginal question

Six speakers, including Ritu and Sandeep, will speak one after another at a seminar. The organisers do not want Ritu and Sandeep to speak one immediately after the other (in either order). How many speaking orders are possible?

Options for question 27

Show the answer and explanation
CorrectNot quiteAnswer D

Correct answer: D

Explanation

  1. All orders: 6!=7206! = 720.

  2. Orders with the two together: treat them as a block, 5!×2=2405! \times 2 = 240.

  3. Orders with them apart =720−240=480= 720 - 240 = 480.

Worth noting

240 is the number of orders where they ARE together. 360 simply halves 720, and 120 is 5!5! without the factor 2.

Concept
Counting 'never together' by subtracting 'together' from the total
Typical time
70 s
Your time
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The rule this testsArrangements and selections
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