SOLUTION: Vince has eight Algebra books and five Statistics books. He only has space for five books on the shelf. If the first four slots are to be occupied by Algebra books and the last slo

Question 1190636: Vince has eight Algebra books and five Statistics books. He only has space for five books on the shelf. If the first four slots are to be occupied by Algebra books and the last slot is to be occupied by s Statistics book, in how many ways can this be done?

Found 2 solutions by math_tutor2020, ikleyn:
Answer by math_tutor2020(3816) (Show Source): You can put this solution on YOUR website!

I'll assume that order matters. If your teacher insists order doesn't matter, then ignore this current section and skip to the next section below.

If order matters, then we have 8*7*6*5 = 1680 different permutations for the algebra books.
I started with 8 and counted down by 1 each time, multiplying along the way. I stopped once I had 4 slots filled.

We then have 5 choices for the stats book chosen, so overall there are 1680*5 = 8400 different ways to arrange the books if order matters for the algebra books.

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If order doesn't matter, then we divide that 1680 by 4! = 4*3*2*1 = 24 to get 1680/24 = 70

We divided by 24 because there are 24 ways to arrange any set of four items.
Something like {A,B,C,D} is the same as {B,A,C,D}.

We have 70 different combinations of picking 4 books from a pool of 8 total.

There are 70*5 = 350 ways to arrange the books if order doesn't matter for the algebra books.

Answer by ikleyn(52776) (Show Source): You can put this solution on YOUR website!
.
Vince has eight Algebra books and five Statistics books. He only has space for five books on the shelf.
If the first four slots are to be occupied by Algebra books and the last slot is to be occupied by
Statistics book, in how many ways can this be done?
~~~~~~~~~~~~~~

Any of 8 Algebra books at the 1st spot; any of the remaining 7 Algebra books at the 2nd spot; any of . . . and so on . . . give, in all, 8*7*6*5 = 1680 permutations for Algebra books at four first slots. Next, there are 5 choices to select a Statistic book to place it at the last, fifth spot. It gives the ANSWER : there are 1680*5 = 8400 possible ways to arrange his books under given conditions.

Solved.

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