Question 1162135
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<pre>

The answer is  8*5!*7! = 8*(5*4*3*2*1)*(7*6*5*4*3*2*1) = 4838400.


<U>Explanation</U>


We consider the group of 5 males as one object.



There are 8 possible positions/places for this group, considered as a single  object, in the row of 7 females.

    It gives the first factor of 8 in the formula.



Next, there are 5! ways to order 5 males inside their group.

    It gives the factor 5! in the formula.



Finally, there are 7! ways to order 7 females inside their group.

    It gives the factor 7! in the formula.



All these elementary arrangements are INDEPENDENT - - - so, we take the product of the factors to get the answer.
</pre>

Solved, completed, answered and explained.


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See the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =http://www.algebra.com/algebra/homework/Permutations/Introduction-to-Permutations.lesson>Introduction to Permutations</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =http://www.algebra.com/algebra/homework/Permutations/PROOF-of-the-formula-on-the-number-of-permutations.lesson>PROOF of the formula on the number of Permutations</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =http://www.algebra.com/algebra/homework/Permutations/Problems-on-Permutations.lesson>Simple and simplest problems on permutations</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =https://www.algebra.com/algebra/homework/Permutations/Special-type-permutations-problems.lesson>Special type permutations problems</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =https://www.algebra.com/algebra/homework/Permutations/How-many-different-permutations-may-exist-ubder-given-restrictions.lesson>Problems on Permutations with restrictions</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =https://www.algebra.com/algebra/homework/Permutations/Fundamental-counting-principle-problems.lesson>Fundamental counting principle problems</A> 

in this site.


Also, &nbsp;you have this free of charge online textbook in ALGEBRA-II in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this online textbook under the topic &nbsp;"<U>Combinatorics: Combinations and permutations</U>". 



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