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Sagot :
Ribbon Photo Ribbon Ribbon Photo Ribbon
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Answer:
Combination of ribbons and photos will fit side by side with no overlap on Lexi's bulletin board are 27.
Step-by-step explanation:
Given : Lexi's bulletin board is 40 centimeters wide. Each of her ribbons is 4 centimeters wide, and her photos are 12 centimeters wide.
To find : What combination of ribbons and photos will fit side by side with no overlap on Lexi's bulletin board?
Solution :
Lexi's bulletin board is 40 centimeters wide.
Ribbons is 4 centimeters wide.
Photos are 12 centimeters wide.
Now, The ways 40 divides in 12 and 4 are
1) 7 ribbons- 4 cm and 1 Photo - 12 cm (RRRRRRRP)
i.e, [tex]7\times 4+1\times 12=28+12=40[/tex]
These were arranged as
[tex]\frac{8!}{7!\times 1!}=\frac{8\times 7!}{7!}=8[/tex]
2) 4 ribbons- 4 cm and 2 Photo - 12 cm (RRRRPP)
i.e, [tex]4\times 4+2\times 12=16+24=40[/tex]
These were arranged as
[tex]\frac{6!}{4!\times 2!}=\frac{6\times5\times 4!}{4!\times 2\times 1}=15[/tex]
3) 1 ribbons- 4 cm and 3 Photo - 12 cm (PPPR)
i.e, [tex]1\times 4+3\times 12=4+36=40[/tex]
These were arranged as
[tex]\frac{4!}{3!\times 1!}=\frac{4\times 3!}{3!\times 1}=4[/tex]
Total combinations of ribbons and photos are 8+15+4=27.
Therefore, Combination of ribbons and photos will fit side by side with no overlap on Lexi's bulletin board are 27.
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