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
Is urgent What is the equation of the line, in point-slope form, that goes through (2, -1)
Pavlova-9 [17]

Answer:

c. y + 1 = -⅕(x - 2)

Step-by-step explanation:

To write the equation in point-slope form, we need to know the slope (m) and coordinates of a point the line passes through.

The equation would be in the form of y - b = m(x - a).

(a, b) = (2, -1)

Since the line is perpendicular to y = 5x + 3, the slope will be the negative reciprocal of 5 which is -⅕

m = -⅕.

Substitute a = 2, b = -1, and m = -⅕ into y - b = m(x - a).

Thus:

y - (-1) = -⅕(x - 2)

y + 1 = -⅕(x - 2)

7 0
2 years ago
How do you write 1.7 in expanded form
olga2289 [7]
<span>1.7 = (1 x 1) + (7/10)

Hope this helps! Could I gent a Brainliest?
</span>
7 0
3 years ago
Read 2 more answers
What is the vertex of a parabola defined by the equation <br> x = 5y2?
QveST [7]

Find the critical points of f(y):Compute the critical points of -5 y^2
To find all critical points, first compute f'(y):( d)/( dy)(-5 y^2) = -10 y:f'(y) = -10 y
Solving -10 y = 0 yields y = 0:y = 0
f'(y) exists everywhere:-10 y exists everywhere
The only critical point of -5 y^2 is at y = 0:y = 0
The domain of -5 y^2 is R:The endpoints of R are y = -∞ and ∞
Evaluate -5 y^2 at y = -∞, 0 and ∞:The open endpoints of the domain are marked in grayy | f(y)-∞ | -∞0 | 0∞ | -∞
The largest value corresponds to a global maximum, and the smallest value corresponds to a global minimum:The open endpoints of the domain are marked in grayy | f(y) | extrema type-∞ | -∞ | global min0 | 0 | global max∞ | -∞ | global min
Remove the points y = -∞ and ∞ from the tableThese cannot be global extrema, as the value of f(y) here is never achieved:y | f(y) | extrema type0 | 0 | global max
f(y) = -5 y^2 has one global maximum:Answer: f(y) has a global maximum at y = 0

3 0
3 years ago
If x= -4, find the value of x²-5+6.​
lbvjy [14]

Answer:

42 is your answer if there is -5x

Step-by-step explanation:

when x=-4

x²-5x+6=(-4)²-5×-4+6=16+20+6=42

3 0
2 years ago
Read 2 more answers
Chan deposited money into his retirement account that is compounded annually at an interest rate of 7%. Chan thought the equival
dedylja [7]

Answer:

No, equivalent quarterly rate will be approx 1.75%

Step-by-step explanation:

Given that Chan deposited money into his retirement account that is compounded annually at an interest rate of 7%.

We know that there are 4 quarters in 1 year.

So to find that equivalent quarterly we will divide given yearly rate by number of quarters.

That means divide 7% by 4.

which gives 1.75%.

But that is different than Chan's though of 2% quarterly interest.

Hence Chan is wrong.

4 0
3 years ago
Other questions:
  • So far, 907907907 of the 122312231223 voters have agreed to the new amendment. Based on this data, what is a reasonable estimate
    14·2 answers
  • The perimeter of a pool table is 30 feet. The table is twice as long as it is wide. What is the length of the pool table?
    7·1 answer
  • True or false 1-5 and u don’t really need to explain them that much.
    8·1 answer
  • Larry, joe, and curly decided to buy there mother a new computer so she could keep up with her friends. The cost of the computer
    14·1 answer
  • A recipe that makes 5 dozen cookies calls for 4 eggs and 2 cups of flour. Matthew only has 2 eggs. a) How much flour should he u
    7·1 answer
  • A box is 50 cm long. Which of these is closest to the length of this box in feet? (1 inch = 2.54 cm)
    7·2 answers
  • Hello peepers! I need help ASAP please. Thanks!
    11·1 answer
  • Quadrilateral ABCD, shown below, is translated 3 units to the left to create quadrilateral A'B'C'D'.
    9·1 answer
  • The system of inequalities,
    12·1 answer
  • a right triangle has legs measuring 20 in. and 28 in. what is the length of the hypotnuse? round to the nearest tenth.
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!