SOLUTION: Twelve presidents, 5 males and 7 females, attending a summit on climate decide to conclude the summit with a photo shoot. In how many ways different can they arrange themselves in

Question 1162135: Twelve presidents, 5 males and 7 females, attending a summit on climate decide to conclude the summit with a photo shoot. In how many ways different can they arrange themselves in a single row, if the males must be kept together?

Answer by ikleyn(52908) (Show Source): You can put this solution on YOUR website!
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The answer is  8*5!*7! = 8*(5*4*3*2*1)*(7*6*5*4*3*2*1) = 4838400.


Explanation


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.

Solved, completed, answered and explained.

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See the lessons
    - Introduction to Permutations
    - PROOF of the formula on the number of Permutations
    - Simple and simplest problems on permutations
    - Special type permutations problems
    - Problems on Permutations with restrictions
    - Fundamental counting principle problems
in this site.

Also, you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Combinatorics: Combinations and permutations".

Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.

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