Maharashtra State BoardHSC Science (Electronics) 11th
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A committee of 10 members sits around a table. Find the number of arrangements that have the president and the vice-president together. - Mathematics and Statistics

Sum

A committee of 10 members sits around a table. Find the number of arrangements that have the president and the vice-president together.

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Solution

Here, n = No. of committee members = 10

Consider 'President' and 'Vice-President' as one unit.

So there are 1 + 8 = 9 members to be arranged around a table.

Such arrangements are (9 – 1)! = 8! and corresponding to each of these 8! arrangements, the President and the Vice-President can interchange their places in 2! ways.

∴ the total number of circular arrangements of 10 committee members in which President and Vice-President sit together

= 8! × 2!

= 2(8!)

Concept: Concept of Permutations - Circular Permutations
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APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) 11th Standard Maharashtra State Board
Chapter 3 Permutations and Combination
Exercise 3.5 | Q 5 | Page 61
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