Question

lexi's bulletin board is 40 centimeters wide. each of her ribbons is 4 centimeters wide, and her photos are 12 centimeters wide. what combination of ribbons and photos will fit side by side with no overlap on Lexi's bulletin board.

Answer 1

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,   $7\times 4+1\times 12=28+12=40$    

These were arranged as

$\frac{8!}{7!\times 1!}=\frac{8\times 7!}{7!}=8$

2) 4 ribbons- 4 cm and 2 Photo - 12 cm (RRRRPP)

i.e,   $4\times 4+2\times 12=16+24=40$    

These were arranged as

$\frac{6!}{4!\times 2!}=\frac{6\times5\times 4!}{4!\times 2\times 1}=15$

3) 1 ribbons- 4 cm and 3 Photo - 12 cm (PPPR)

i.e,   $1\times 4+3\times 12=4+36=40$

These were arranged as

$\frac{4!}{3!\times 1!}=\frac{4\times 3!}{3!\times 1}=4$    

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.

Answer 2

Ribbon Photo Ribbon Ribbon Photo Ribbon

I think hope i helped!! Xx