[tex]\huge{\mathbb{\tt{QUESTION↓}}}[/tex]
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.
[tex]\huge{\mathbb{\tt{SOLUTION↓}}}[/tex]
[tex]\textsf{ Given that: M=5 , S=4 , E=3}[/tex]
[tex]\begin{gathered}\\\end{gathered} [/tex]
[tex]\textsf{ Using the Linear Permutation:} [/tex]
For Mathematics=5
[tex]\sf{P=n!}P=n![/tex]
[tex]\sf{P=5!}P=5![/tex]
[tex]\sf{P=5×4×3×2×1}[/tex]
[tex]\sf{P=120}[/tex]
[tex]\begin{gathered}\\\end{gathered}[/tex]
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For Science=4
P=n!}
P=4!
P=4×3×2×1
P=24
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For English=3
P=n!
P=3!
P=3×2×1
P=6
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Multiply all the permutations:
P=120×24×6
P=17,280
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[tex]\huge{\mathbb{\tt{ANSWER↓}}}[/tex]
There are 17,280 ways we can arrange in a shelf.
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