how many ways are there for eight men and five women to stand in a line so that no tow women stand right next to each other

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30-11-2022
Mathematics

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how many ways are there for eight men and five women to stand in a line so that no tow women stand right next to each other

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Tutorconsortium325 Tutorconsortium325 · Answer 1 · 2022-12-05T04:04:54+01:00

There are therefore 609638400 different ways to arrange eight men and five women in a line so that no two women are positioned adjacent to one another.

What is fundamental counting principle?

The basic counting principle is a method for keeping track of all the potential outcomes in a situation. It states that there are n*m ways to carry out both of these activities if there are n ways to carry out one action and m ways to carry out another action after that.

Here,

Number of ways men can stand,

=8!

=40320 ways

Number of ways women are standing,

=9P5

As shown in the image,

=15120 ways

For arranging both of them,

=40320*15120

=609638400 ways

So there is 609638400 ways of arranging eight men and five women to stand in a line so that no two women stand right next to each other.

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