Permutations and Combinations

Question

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 1

1) 

(i) In this case order of the books does not matter, therefore we're to use combination formula.

8!/(6!*(8-6)!)=8*7*6*5*4*3/(6*5*4*3*2)=28

 

The problem with clock.(not marked)

Here an order of books matters.  Thus we need a permutation formula. I will split the problem in 2 stages: at first consider book permutations, and then add the clock.

Book permutations: 3*2*1=6. 

Adding the clock: there are two places for the clock because we are required to have books on each side of it. Hence with the already computed book permutations we can double our number of displays on the shelf:6*2=12.

 

(i) The question is not clear. What 8 books, from the very first problem (i)? There were no restrictions. 

(ii) Again, your question is not clear. What 8 books, from the very first problem or from the problem with the clock on the shelf?