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Flura [38]
3 years ago
12

In how many ways can I distribute $6$ identical cookies and $6$ identical candies to $4$ children, if each child must receive ex

actly $3$ items?
Mathematics
2 answers:
AysviL [449]3 years ago
7 0

Answer: 44

The only choice to be made is how many gummy bears to give each child; once we've decided that, each child must receive the unique number of candies that will bring their total to 3 items. Thus, our problem reduces to counting integer solutions to a+b+c+d=6 that satisfy 0 <= a, b, c, d <= 3.

Ignoring the <= 3 restrictions, we have 9C3 = 84 solutions (which correspond to arrangements of 6 objects and 3 dividers).

Now we correct for the overcount. We must reject 5C3 = 10 solutions satisfying a >= 4, as well as 10 solutions with b, c, d >= 4. No further correction is needed, as it is not possible for more than one of a, b, c, d to be greater than or equal to 4.

Thus there are 84 - 4 x 10 = 44 ways to distribute the gummy bears, each of which forces a unique distribution of candies. There are 44 solutions.

But you guys should USE THE MESSAGE BOARD as well if you have trouble with AoPS HW problems.

(Solution from AoPS)

Hope that helped,

-sirswagger21

Olegator [25]3 years ago
3 0
Should distribute 2 cookies 1 candy and 2 candies 1 cookie I believe
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During a basketball practice, Mai attempted 49 free throws and was on 25% of them. How many successful free throws did she make?
Brrunno [24]

Mai made 12 successful free throws.

Step-by-step explanation:

Given,

Free throws made by Mai = 49 free throw

Successful throws = 25%

Number of successful throws = 25% of free throws

Number of successful throws = \frac{25}{100}*49

Number of successful throws = \frac{1225}{100} = 12.25

Rounding off to nearest whole number;

Number of successful throws = 12

Mai made 12 successful free throws.

Keywords: percentage, division

Learn more about division at:

  • brainly.com/question/11150876
  • brainly.com/question/11175936

#LearnwithBrainly

6 0
3 years ago
A recipe requires 3 cups of flour to make 27 dinner rolls. How much flour is needed to make 9 rolls.
amid [387]
9 rolls* (3 cups of flour/ 27 dinner rolls)= 1 cup of flour.

1 cup of flour is needed to make 9 rolls~
5 0
3 years ago
-5X +1 92 - 321+13 - 12X
Bogdan [553]

Answer:

Step-by-step explanation:

There’s no equal sign.

8 0
3 years ago
2x3 + x2 + 7x - 6)-(- 2x + 10x + 10x+9)​
AVprozaik [17]

Answer:

2x³ + x² - 11x - 15

Step-by-step explanation:

Step 1: Write out expression

2x³ + x² + 7x - 6 - (-2x + 10x + 10x + 9)

Step 2: Distribute negative

2x³ + x² + 7x - 6 + 2x - 10x - 10x - 9

Step 3: Combine like terms (x)

2x³ + x² + 9x - 10x - 10x - 9 - 6

2x³ + x² - x - 10x - 9 - 6

2x³ + x² - 11x - 9 - 6

Step 4: Combine like terms (constants)

2x³ + x² - 11x - 15

5 0
3 years ago
18+2(4-1) equation please help!
77julia77 [94]

Answer:

18+2(4−1)

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3 years ago
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