In how many ways 5 gentlemen and 3 ladies arrange themselves around a round table
arvindmkt12:
In What way they have to be arranged
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We got such 8 ways.
Now, let's suppose that these men as well as women are no more identical.
Now we can call them G1, G2,..... & L1, L2,....
Think of any of the 8 ways we found. First let's think about men.Keep positions of G1 & G2 fixed & reverse the positions of G3, G4 & G5. You will get such 6 positions. Keep only position of G1 fixed. Placing other gents in place of G2, you will get 6×3=18 more positions. For the fixed position of G1, we have 24 ways.
So thinking of only gents, we have 24×5=120 positions.
Now let's think of women. You can easily find 6 different positions of women as there are only 3 ladies.
So, for every position of gents, there are 6 positions of ladies.
So, we have 120×6=720 positions.
Now recall our first 8 ways.
So, in all we have 720×8= 5760 ways.
As this question is very confusing, I may have committed some mistakes. If you find them, please point out.
Now, let's suppose that these men as well as women are no more identical.
Now we can call them G1, G2,..... & L1, L2,....
Think of any of the 8 ways we found. First let's think about men.Keep positions of G1 & G2 fixed & reverse the positions of G3, G4 & G5. You will get such 6 positions. Keep only position of G1 fixed. Placing other gents in place of G2, you will get 6×3=18 more positions. For the fixed position of G1, we have 24 ways.
So thinking of only gents, we have 24×5=120 positions.
Now let's think of women. You can easily find 6 different positions of women as there are only 3 ladies.
So, for every position of gents, there are 6 positions of ladies.
So, we have 120×6=720 positions.
Now recall our first 8 ways.
So, in all we have 720×8= 5760 ways.
As this question is very confusing, I may have committed some mistakes. If you find them, please point out.
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