Question 1196436
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<U>ANSWER</U>.  k! = 1*2*3* . . . *(k-1)*k.



<U>Explanation</U>.


Let the sets be A and B: they have equal numbers of elements.


1st element of A can be related to any of k elements of B.

2nd element of A can be related to any of remaining (k-1) elements of B.

3rd element of A can be related to any of remaining (k-2) elements of B.


   . . . and so on . . . 


It gives the answer.
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Solved and explained.


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The problem is the same as to ask 


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        " how many are there permutations of a set of k elements ? "
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