SOLUTION: In how many ways can seven books be arranged on a shelf if a)the books are different and the mathematics book must be on an end? b) the books are different and four particular bo

Algebra ->  Permutations -> SOLUTION: In how many ways can seven books be arranged on a shelf if a)the books are different and the mathematics book must be on an end? b) the books are different and four particular bo      Log On


   

Question 875356: In how many ways can seven books be arranged on a shelf if
a)the books are different and the mathematics book must be on an end?
b) the books are different and four particular books must be together?
Thank you!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
a)

The last slot is for the math book. So you really have 7-1 = 6 books to place in 7-1 = 6 slots.

This gives you 6! = 6*5*4*3*2*1 = 720 ways to do this (order matters).

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b)

Group the 4 books and think of them as one book. Maybe you can bind them up with plastic wrap or something.

So you really have 7-4+1 = 4 "books" (3 individual books + the group of 4 books)

Arranging these "books" gives you 4! = 4*3*2*1 = 24 ways to do this.

Now since you can arrange the books in the plastic binding (ex: ABCD is one way, BACD is another), this means you have 4! = 24 ways to arrange them.

So you really have 4!*4! = 24*24 = 576 ways to arrange the 7 books where 4 particular books must be together.