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1. in how many ways can you arrange five mathematics books,four science books,and three english books, on a shelf such as that books of the same subject are kept together.

For Mathematics=5

-------------------------------------------------------------------------------- For Science=4

P=n!}

P=4!

P=4×3×2×1

P=24

--------------------------------------------------------------------------------For English=3

P=n!

P=3!

P=3×2×1

P=6

--------------------------------------------------------------------------------

Multiply all the permutations:

P=120×24×6

P=17,280

--------------------------------------------------------------------------------

There are 17,280 ways we can arrange in a shelf.

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