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

Question 1131118: in how many ways can 10 people seated on a bench if only 5 are seats are available
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
.
in how many ways can 10 people seated on a bench if only 5 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.

RELATED QUESTIONS
in how many ways can 10 people seated on the bench if only four seats are available? (answered by checkley79)

in how many ways can nine people be seated on a bench if only three seats are... (answered by Theo)

In how many ways can 9 people be seated on a bench if only 3 places are available? (answered by Fombitz)

In how many ways can 7 people seated on a sofa if there are only 4 seats available? (answered by reviewermath)

In how many ways five people be seated on a sofa if there are only three seats... (answered by stanbon)

In how many ways can 6 people be seated on a sofa if there are 3 seats available... (answered by solver91311)

if 5 people want to be seated, in how many ways can 4 of them be seated on a bench that... (answered by dfrazzetto)

On a bench that seats five people, how many ways can five people be... (answered by Alan3354,edjones)

1) In how many ways can 5 seats on a bench be assigned from amongst 12 people? 2)John... (answered by stanbon)