Rachel has ribbons that are blue, green, red, orange, and ye

Question

Rachel has ribbons that are blue, green, red, orange, and yellow. To identify the plants in her garden, she ties either 1 ribbon, or 2 ribbons of different colors, to each plant. How many different plants can Rachel label in this way without labeling more than one plant the same way?

A. 5
B. 10
C. 15
D. 20
E. 25

A. 5
B. 10
C. 15
D. 20
E. 25

Zarrolou · Answer

Number of plants identified by one color= 5.

Number of plants identified by a combination of 2 colors=  5C2=10

Total number =  5+10=15.

VeritasPrepRon · Answer

I really like questions like this because they can bait you into doing more math than necessary. The combinatorics formula (  \frac{n!}{k!(n-k)!} ) will yield the right answer here if you apply it to both the 1-ribbon(  \frac{5!}{4!1!} ) and 2-ribbon possibilities ( \frac{5!}{3!2!} ). The first formula will yield 5, and the second one will end up giving 10, so that's 15 total possibilities. Answer choice C.

You can get the answer pretty quickly using the formula, but if you're not comfortable with formulas, feel free to write out the possibilities logically. Any of the five colors works for the 1-ribbon strategy, so the only question is for the 2-colors. If I start with blue, I can add a green, red, orange, or yellow ribbon, and get 4 possibilities. I've now done everything I can with blue, because blue-blue isn't allowed and blue-green and green-blue is the same thing (especially if a gust of wind turns the plant around!). So we're done with blue, on to green! I can add red, orange or yellow to green, so that's 3 more choices. Now green is done, so the next choices are red-orange or red-yellow for 2 more options. The final choice is orange-yellow, so 1 more. The total is 4+3+2+1, which is a pretty obvious pattern when you write them out. Adding back the five monochromatic options, and the final answer is 15, or C).

The explanation for writing out choices may have been longer than the combinatory formula, but it's often much more intuitive and less error-prone. Feel free to write out the options if it's a reasonable amount, or extrapolate the choices logically if it's not. The formula is very helpful here, but not at all necessary for solving the question.

Hope this helps!
-Ron

Asifpirlo · Answer

...........
solution:
using only one in each plant = 5C1 = 5
using two ribbons in each plant = 5C2 = 10 (different colors is the topic here not their arrangement, so combination).

total plants = 15

Bunuel · Answer

Similar question to practice: a-certain-office-supply-store-stocks-2-sizes-of-self-stick-92842.html

luisdicampo · Answer

Deconstructing the Question

Rachel has  5 colors  available and can label each plant using either  1 ribbon  OR  2 ribbons  of different colors.

1. Using 1 Ribbon  
She simply picks 1 color out of 5.
 Ways = 5C1 =    5

2. Using 2 Ribbons  
She picks a group of 2 colors out of 5. Order does not matter for the identification.
 Ways = 5C2 = (5 * 4) / 2 =    10

3. Total Distinct Ways  
Sum the two mutually exclusive scenarios:
 Total = 5 + 10 =    15

The correct answer is C.

Rachel has ribbons that are blue, green, red, orange, and ye

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Rachel has ribbons that are blue, green, red, orange, and ye

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