. There is meeting of 20 delegates that is to be held in a hotel. In how many ways these delegates can be seated along a round table, if three particular delegates always seat together? 17! 3! 18! 3! 17! 4! 18! 4!
Question
. There is meeting of 20 delegates that is to be held in a hotel. In how many ways these delegates can be seated along a round table, if three particular delegates always seat together? 17! 3! 18! 3! 17! 4! 18! 4!
Solution
The question is asking for the number of ways 20 delegates can be seated around a round table, with the condition that three particular delegates must always sit together.
Here's how to solve it:
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Consider the three particular delegates as one unit. So now we have 18 units (15 individual delegates + 1 unit of 3 delegates) to arrange.
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In a round table, the number of arrangements is (n-1)!. So, the 18 units can be arranged in 17! ways.
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The three particular delegates can arrange themselves in 3! ways.
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Therefore, the total number of arrangements is 17! * 3!.
So, the correct answer is 17! 3!.
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