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
Dilations PLEASE HELP ME PLEASE
AURORKA [14]

Answer:

D' (6, - 6 )

Step-by-step explanation:

Assuming the dilatation is centred at the origin then multiply the coordinates of D by 3, that is

D (2, - 2 ) → D'(3 × 2, 3 × - 2 ) → D' (6, - 6 )

6 0
3 years ago
In which picture is point A at 34?
tekilochka [14]
There’s no picture..
5 0
3 years ago
Which one??? I need help. Be serious please
Talja [164]

Answer:

c

Step-by-step explanation:

10+12=22

=22^2

=484

4 0
3 years ago
Read 2 more answers
The formula Y=X⁴-4X³+3X² is growing?
miskamm [114]

Answer:

The best way to know weather the formula y=x⁴-4x³+3x² is growing or not, is by graphing it.

As you can see in the attached picture:

  • For -inf<x< 0 the graph decreases.
  • For 0<x<0.634 the graph is growing
  • For 0,634<x<2.366 the graph decreases
  • For 2.366<x<+inf the graph is growing.

Therefore, the polynomial grows in the intervals stated before.

6 0
3 years ago
Yolonda withdrew 60 dollars from her checking account.Write a signed number to represent this change in her account.
JulsSmile [24]

Answer:

$ 60.00

Step-by-step explanation:

.

8 0
2 years ago
Other questions:
  • Find the average of 60 75 88 and 93
    14·1 answer
  • Which number is 7.323 rounded to the nearest tenth? A 7.3 6 74 © 7.32 07.33
    13·1 answer
  • Analyze the conditional statement below and complete the instructions that follow. You will receive the trophy if you win the ch
    10·2 answers
  • In a right triangle one leg measures a quarter of the other, how much do its acute angles measure? with procedure please​
    14·1 answer
  • I need help solving the problem.
    15·1 answer
  • 7. A sphere has a volume of 361 in. Find the<br>radius of the sphere.​
    9·1 answer
  • Which digit has the greatest value in the number 1,567
    8·1 answer
  • What is the domain and derivative of f(x)=ln(2xsqrt(2+x))?
    8·1 answer
  • What is the y-intercept of y=-3x + 6?<br> O 6<br> -3<br> 3<br> 0 6
    10·1 answer
  • Determine what type of model best fits the given situation: principal p is invested at an annual interest of rate r, compounded
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!