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# I have 7 different math books and 4 different history books. In how many ways can I line the 11 books up on a shelf if a history book must b

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I have 7 different math books and 4 different history books. In how many ways can I line the 11 books up on a shelf if a history book must be in the middle and each end must be a math book?

Apr 13, 2015

#2
+95334
+5

I have 7 different math books and 4 different history books. In how many ways can I line the 11 books up on a shelf if a history book must be in the middle and each end must be a math book?

M -  - - - H - - - - M           Total of 7 maths and 4 history and all are different

first*last*middle* rest(8)

7*6*4*8*7*6*5*4*3*2*1 = 7*6*4*8! =6,773,760

I think that is the same a Geno :)

Apr 14, 2015

#1
+17747
+5

The first location (on the left) will hold one of the 7 math books.

The last location (on the far right) will hold one of the remaining 6 math books.

The middle location (location 6) will hold one of the four history books.

There are 8 books remaining.

In location #2 (from the left), place one of the 8 remaining books.

In location #3, place one of the 7 remaining books.

In location #4, place one of the 6 remaining books.

In location #5, place one of the 5 remaining books.

Location #6 is filled with the previously chosen history book.

In location #7, place one of the 4 remaining books.

In location #8, place one of the 3 remaining books.

In location #9, place one of the 2 remaining books.

In location #10, place the last book.

To find the total number of possibilities, multiply these numbers together:

7 x  8 x 7 x 6 x 5 x 4 x 4 x 3 x 2 x 1 x 6

Apr 13, 2015
#2
+95334
+5

I have 7 different math books and 4 different history books. In how many ways can I line the 11 books up on a shelf if a history book must be in the middle and each end must be a math book?

M -  - - - H - - - - M           Total of 7 maths and 4 history and all are different

first*last*middle* rest(8)

7*6*4*8*7*6*5*4*3*2*1 = 7*6*4*8! =6,773,760

I think that is the same a Geno :)

Melody Apr 14, 2015