Let A= { x 1 , x 2 , x 3 , x 4 , x 5 , x 6 , x 7 , x 8 } , B= { y 1 , y 2 , y 3 , y 4 } . The total number of function f : A → B that are onto and there are exactly three elements x in A such that f ( x )= y1 is?
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Pick the three elements that map to $y_1$. Then, pick an onto function from the remaining elements of $A$ to the remaining elements of $B$. Apply rule of product and conclude. – JMoravitz May 09 '23 at 12:13