+0

# help!

0
399
2

A lecture hall contains 20 chairs, all lined in a row. What is the number of ways that five chairs can be chosen, so that no two chairs are adjacent?

Aug 7, 2020

#1
0

By stars and bars, the number of ways is C(15,4) = 1365.

Aug 7, 2020
#2
+114522
+1

A lecture hall contains 20 chairs, all lined in a row. What is the number of ways that five chairs can be chosen, so that no two chairs are adjacent?

There will be 4 children each with an empty chair on their right, that is 8 seats taken.   But since they are tied in pairs, it is just 4 positions gone.

The fifth child will sit to the very right of all the others but there may not be an empty chair to his right.  So now there are 9 seats but just 5 positions taken.

There are now 11 seats left that all have their own position.

So there are 16 positions in total and I want to decide where the 11 can go.

So that is 16C11 = 16C5 = 4368

so I think there re 4368 arrangements and that is assuming that all the chairs are identical and all the children are identical.

Aug 7, 2020