In how many different ways a group of 4 men and 4 women be formed out of 7 men and 8 women
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Group of 4 men and 4 women = Group of 8 people.
Suppose we have 8 vacant places for 4 men and 4 women.
_,_,_,_,_,_,_,_
Now, let the first four places be for men.
First place has possiblities of 7 men sitting on it, second place has 6, 3rd place has 5 and 4th place has 4.
Let the last 4 places be vacant be for women.
First place can be filled by 8 women, 2nd place by 7, 3rd place by 6 and 4th place by 5.
So, total number of trials is :-
7x6x5x4x8x7x6x5
So, total number of arrangements here is
1,411,200
Suppose we have 8 vacant places for 4 men and 4 women.
_,_,_,_,_,_,_,_
Now, let the first four places be for men.
First place has possiblities of 7 men sitting on it, second place has 6, 3rd place has 5 and 4th place has 4.
Let the last 4 places be vacant be for women.
First place can be filled by 8 women, 2nd place by 7, 3rd place by 6 and 4th place by 5.
So, total number of trials is :-
7x6x5x4x8x7x6x5
So, total number of arrangements here is
1,411,200
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1
Answer:
2450
(7c4×8c4)=
(7×6×5/3×2×1)(8×7×6×5/4×3×2×1)
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