Xyrielmonsantoidn
Answered

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3. What is the number of possible arrangements of nine books on a
shelf where four Algebra books are of the same kind, three
Geometry books are of the same kind, and two Statistics books
are of the same kind?​

Sagot :

AGboiiidn

[tex] \large\underline \mathcal{{QUESTION:}}[/tex]

3. What is the number of possible arrangements of nine books on a shelf where four Algebra books are of the same kind, three Geometry books are of the same kind, and two Statistics books are of the same kind?

[tex]\\[/tex]

[tex] \large\underline \mathcal{{SOLUTION:}}[/tex]

The possible arrangments of Algebra:

[tex] \sf P(n,n)=n! \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf P(4,4)=4! \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \: \: \: \: \: \: \: \sf P(4,4)=4 \times 3 \times 2 \times 1 \\ \sf P(4,4)= \boxed{24} \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex]\\[/tex]

The possible arrangements of Geometry

[tex] \sf P(n,n)=n! \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf P(3,3)=3! \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \: \: \: \: \: \: \: \sf P(3,3)= 3 \times 2 \times 1 \: \: \: \: \: \: \: \: \\ \sf P(3,3)= \boxed{6} \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex]\\[/tex]

The possible arrangements of Statistics

[tex] \sf P(n,n)=n! \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf P(2,2)=2! \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \: \: \: \: \: \: \: \sf P(2,2)=2 \times 1 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf P(2,2)= \boxed{4} \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex]\\[/tex]

The possible arrangements of the three books

[tex] \sf P(n,n)=n! \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf P(3,3)=3! \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \: \: \: \: \: \: \: \sf P(3,3)= 3 \times 2 \times 1 \: \: \: \: \: \: \: \: \\ \sf P(3,3)= \boxed{6} \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex]\\[/tex]

Multiply all the outcomes:

[tex] \sf P =24 \times 6 \times 4 \times 6 \\ \boxed{ \sf P=3456} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex]\\[/tex]

[tex] \large\underline \mathcal{{ANSWER:}}[/tex]

  • There are 3456 ways
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