Question 1131118
.
in how many ways can 10 people {{{highlight(be)}}} seated on a bench if only 5 {{{highlight(cross(are))}}} seats are available 
~~~~~~~~~~~~~~~~~~~~~~



 . . . In other words,  in how many ways can  5  people be selected from  10  people and ordered . . . 



<U>Answer</U>.  &nbsp;&nbsp; In  &nbsp;10*9*8*7*6 = 30240 &nbsp;ways.



<U>Solution</U>


<pre>
Any of the 10 persons can be placed on the seat #1;

any of the remaining 9 persons can be placed on the seat #2;

any of  ------------ 8 ---------------''---------------- #3;

any of  ------------ 7 ---------------''---------------- #4;

any of  ------------ 6 ---------------''---------------- #5.


The product of the numbers of these options gives the answer.
</pre>

Solved.


--------------------


You may find millions of similar problems in combinatorics, &nbsp;and all of them are solved in this way.