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2 years ago

how many ways are there to put $4$ balls into $3$ boxes, given that the balls are not distinguished and neither are the boxes?

Mathematics

1 answer:

yawa3891 [41]2 years ago

8 0

Answer:

Step-by-step explanation:

think that there are 15 ways ... call the boxes A, B, and C.

You could put all four b***s into either box A, or box B, or box C ---> 3 ways.

You could put three ball into one box and the other ball into another box:

-- 3 into A, 1 into B, 0 into C; or 3 into A, 0 into B, 1 into C; or 1 into A, 3 into B, 0 into C; or 1 into A, 0 into B, 3 into C; or 0 into A, 3 into B, 1 into C; or 0 into A, 1 into B, 3 into C ---> 6 ways

You could put two balls into one box and the other two balls into another box:

-- 2 into A, 2 into B, 0 into C; or 2 into A, 0 into B, 2 into C; or 0 into A, 2 into B, 2 into C ---> 3 ways.

You could put two b***s into one box and one ball into each of the other two boxes:

-- There are three boxes that could get the two b***s ---> 3 ways

Total: 3 + 6 + 3 + 3 = 15 ways.

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An English professor assigns letter grades on a test according to the following scheme. A: Top 5% of scores B: Scores below the

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Answer:

Grade D score:

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Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 78.8

Standard Deviation, σ = 7.1

We are given that the distribution of scores on test is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

D: Scores below the top 77% and above the bottom 9%

We have to find the value of x such that the probability is 0.77

$P( X > x) = P( z > \displaystyle\frac{x - 78.8}{7.1})=0.77$

$= 1 -P( z \leq \displaystyle\frac{x - 78.8}{7.1})=0.77$

$=P( z \leq \displaystyle\frac{x - 78.8}{7.1})=0.23$

Calculation the value from standard normal z table, we have,

$\displaystyle\frac{x - 78.8}{7.1} =-0.739\\\\x = 73.55$

We have to find the value of x such that the probability is 0.09

$P(X < 0.09) = \\\\P( X < x) = P( z < \displaystyle\frac{x - 78.8}{7.1})=0.09$

Calculation the value from standard normal z table, we have,

$\displaystyle\frac{x - 78.8}{7.1} = -1.341\\\\x = 69.27$

Thus, the numerical value of score to achieve grade D is

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<h3>How to determine the area</h3>

From the information given, we have the poster to take the form of a rectangle

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Width = 10 inches

Substitute into the formula

Area = 16 × 10

Area = 160 inches square

Thus, the area of the small poster is 160 inches square

Learn more about area here:

brainly.com/question/14137384

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