A circle has the mass of 5 grams and a square has the mass of 4 grams. What is the mass of a triangle?
1 answer:
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The <em>correct answer</em> is:
Explanation:
We want all <em>w</em> women to be seated together. There are <em>w</em>! ways to do this.
Since all women are seated together, we consider the as 1 block to be seated with the men.
There are <em>m</em>! ways of arranging the men. However, we also have the 1 block of women to seat; this makes (<em>m</em>+1)! ways to seat the men and block of women.
There are (<em>m</em>+<em>w</em>)! ways to arrange all of the men and women.
This makes our probability
.
For example, if there are 4 men and 3 women:
There are 3! = 6 ways to seat the women together. This makes 1 block of women.
There are 4! = 24 ways to seat the men together. Taking this with the block of women, we have (4+1)! = 5! = 120 ways to seat the men and block of women.
There are (4+3)! = 7! = 5040 ways to arrange 7 people.
This makes our probability 120(6)/5040 = 720/5040.