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Question
Write the number of ways in which iin which 6 men and 5 women can dine at a round table if no two women sit together.
Write the number of ways in which iin which 6 men and 5 women can dine at a round table if no two women sit together.
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Solution
If all 11 persons are to be seated in a round table of 11 positions there are exactly 5 places for women and 6 places for men.
It is given that no two women sit together, 5p5 this can be done in ways.
The remaining 6 positions can be filled by the 6 men in 6p6 ways. so, the fundamental principle of couting, the number of seating arrangements as required is 5p5×6p6=5!×6!
Hence, the number of ways in which 6 men and 5 women can dine at a round table are 5!×6!.
If all 11 persons are to be seated in a round table of 11 positions there are exactly 5 places for women and 6 places for men.
It is given that no two women sit together, 5p5 this can be done in ways.
The remaining 6 positions can be filled by the 6 men in 6p6 ways. so, the fundamental principle of couting, the number of seating arrangements as required is 5p5×6p6=5!×6!
Hence, the number of ways in which 6 men and 5 women can dine at a round table are 5!×6!.
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