SOLUTION: 1) 6 books are to be chosen from 8 different books (i) Find the number of different selections of 6 books that could be made (ans 28) A clock is to be displayed on a shelf with 3

Question 1070897: 1) 6 books are to be chosen from 8 different books
(i) Find the number of different selections of 6 books that could be made (ans 28)
A clock is to be displayed on a shelf with 3 of the 8 different books on each side of it. Find the number of ways this can be done if
(i) there are no restrictions in the choice of books (ans 20160
(ii) 3 of the eight books are music books which have to be kept together (ans 720)
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
(i) The clock makes no difference.
You figure out how to choose the 6 books and line them up,
and then just make a space in the middle of the row of 6 books
to place the clock There are
ways to do it,
permutations of 6 objects taken from a set of 8.

(ii) I interpret that question as meaning that
you cannot pout only 1 or 2 of the music books on the shelf.
It is either all or none of them,
and since excluding those 3 music books leaves us with only
books, and we need 6,
the 3 music books go on the shelf in one of ways:
on the left of the clock, or on the right.
We still need to figure out in which order
(from left to right) we line them up.
That gives us options.
Then, there are the other 5 books
for you to decide what to do w it them.
You need to pick 3, and decide in what order to display them.
That gives you
different options.
All in all there are

ways to do it.

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