1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
castortr0y [4]
3 years ago
14

A bag contains 3 red marbles, 1 green one, 1 lavender one, 3 yellows, and 2 orange marbles. How many sets of five marbles includ

e at most one of the yellow ones?
Mathematics
1 answer:
solniwko [45]3 years ago
8 0
<span>18 marbles altogether. 

Lavender without any yellow: 
1 way to choose the lavender 
14 others that aren't yellow. 
14C4 ways to choose 4 others. So one answer is 1 X 14C4 = 14C4 = 1001, but that's only if the marbles of the same color are distinguishable. 
Since you normally can't tell one colored marble from another, it'll take more work. E.g., labeling the marbles by the initial of their color, and assigning numbers to them, you could have 
1L, 1R, 2R, 3R and 1G 
or 
1L, 1R, 2R, 3R and 2G, and I think you want to consider those the same "set," since one Green marble is as good as another. If that's not the case, then it doesn't make any difference how many marbles there are that aren't yellow. 

So you need to find how many ways you can make up a set of 4 marbles to add to 1L, without any Yellows. 
You can have 
3 Red + 1 other (G or O) -- that makes two ways 
2 Red + 2 others (GG, OO or GO) -- that makes 3 ways 
1 Red + 3 others (GGG, GGO, GOO, or OOO) -- 4 ways. 
That's all the ways with any Red marbles, a total of 2+3+4=9 

Now let's count the ways with Green ones, but no red 
GGGG 
GGG + O 
GG+ OO 
G + OOO 
O+OOO 
That's 5 more ways, for a total of 9+5 = 14 ways 

Now switching to 1 Yellow and no Lavender, you'll have exactly the same 14 ways of adding 4 non-Lavender marbles to the 1 Yellow. 

So the total is 14+14=28 ways. 

Complicated combinatorial problems like this just have to be broken down into all the cases. There may be a convenient formula that can be used from time to time, but in general there's no formula that's going to help in a non-standard problem like this. You almost always have to start, with, "Assume there are 0, 1, 2, .... some max) number of one item..." and go from there. 

The other thing you need to pay attention to is what objects are distinguishable and what aren't, as noted above where 1001 is the (easy to get) answer if the marbles are all different.</span><span>
</span>
You might be interested in
Six students measure the acceleration (in meters per second per second) of object in free fall. The measured values are shown. T
Sunny_sXe [5.5K]
The measured data is
x=[10.56, 9.52, 9.73, 9.80, 9.78, 10.91].

Calculate the mean.
m = (10.56+9.52+9.73+9.80+9.78+10.91)/6 = 10.05

Calculate the deviations from the mean.
k = x - m
   = [0.51, -0.53, -0.32, -0.25, -0.27, 0.86]

Calculate the absolute deviation from the mean.
d= \frac{1}{6} | (0.51-0.53-0.32-0.25-0.27+0.86) | = |1.184\times10^{-15}| \approx 0

Answer: 0

6 0
3 years ago
What is the force required to move a 2,000 kg car with an acceleration of 2 m/s/s?
Airida [17]

We know that According to Newton's Second Law that :

Force acting on an object is equal to the Mass of that Object multiplied by the Acceleration of that Object.

Given Mass of the Car as : 2000 kg

Acceleration of the Car as : 2 m/s²

Force required to move the Car = 2000 × 2 = 4000 Newton

6 0
3 years ago
Read 2 more answers
The whole sale cost of bicycle is $75. There is a mark up of 55%. What is the new sale price of the bike
blsea [12.9K]

Answer:

$116.25

Step-by-step explanation:

10% = $7.50

5% = $3.75

7.50 x 5 = 37.50

37.50 + 3.75 = $41.25

$75 + $41.25 = $116.25

Hope this helps !

8 0
2 years ago
The sale price for a bicycle is $315 dollars. The original price was first discounted by 50% and then discounted an additional 1
Len [333]
This means that the bicycle was discounted in total by 60%, so $315 is 40% of the original price to get 40% to 100% youd multiply it by 2.5 so so the same to the price 315 x 2.5= 787.5
3 0
3 years ago
Read 2 more answers
What do we do to both sides of the equation? X-8=3
Alik [6]

Answer:

\huge\fbox\red{a}\huge\fbox\orange{n} \huge\fbox\pink{s}\huge\fbox\green{w} \huge\fbox\blue{e}\huge\fbox\purple{r}\

  • We'll add 8 to the both side of the equation on order to get the Value of x
  • x -8+8 = 3+8
  • x = 11

~ʆᵒŕ∂ཇꜱꜹⱽẻⱮë

5 0
2 years ago
Read 2 more answers
Other questions:
  • Mitch used 1/4 pounds of beef to make 3/4 liters of beef strong. If Mitch's recipe is for 1 liter of beef stronoff, how many pou
    15·2 answers
  • Three identical coins, labeled A, B, and C in the figure, lie on three corners of a square 10.0 cm on a side. Determine the x co
    7·2 answers
  • I need a guy bsf. I’m real. Message me please
    12·1 answer
  • PLEASE HELP ASAP, I also have other questions i need help with
    9·1 answer
  • Rewrite the equation without absolute value, thanks!
    8·1 answer
  • A banker earns a $75,000 annual salary, a 2,35% commission on any approved loans for the bank’s business customers, and a fee of
    11·1 answer
  • A number cube has 6 different faces, numbered 1 to 6. All faces have an equal probability of being rolled. What is the probabili
    6·1 answer
  • Please help me with the question please ASAP ASAP please please help ASAP ASAP please please help please
    5·1 answer
  • 40 POINTS
    6·2 answers
  • please just help me and give correct answer and not a wrong short answer i need just explanation and please tell me for each ans
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!