SOLUTION: in how many ways can 10 people seated on a bench if only 5 are seats are available

Algebra ->  Permutations -> SOLUTION: in how many ways can 10 people seated on a bench if only 5 are seats are available       Log On


   

Question 1131118: in how many ways can 10 people seated on a bench if only 5 are seats are available
Answer by ikleyn(52903) About Me  (Show Source):
You can put this solution on YOUR website!
.
in how many ways can 10 people highlight%28be%29 seated on a bench if only 5 highlight%28cross%28are%29%29 seats are available
~~~~~~~~~~~~~~~~~~~~~~


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


Answer.    In  10*9*8*7*6 = 30240  ways.


Solution 

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.

Solved.

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

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