SOLUTION: How many ways are there for 5 men and seven women to stand in a line so that three women stand next to each other

From the remote point of view, you consider these 3 women as one clued object.


So the total number of object to permute, from this point of view is  5 + 7 - 2 = 10.


For 10 objects, you have  10! = 10*9*8*7*6*5*4*3*2*1 = 3628800 permutations.


Now, from the close point of view, there are 3! = 3*2*1 = 6 possible permutations inside this group of the 3 women.


It gives the total  6*3628800 = 10886400  possible permutationns.    ANSWER