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There are (n r) different linear arrangements of n balls of which r are black and n-r are white. give a combinatorial explanatio

Vanyuwa [196]

Answer:

$\frac{n!}{r!(n-r)!}$

Step-by-step explanation:

Combinatorial explanation:

The n balls have to be arranged in n positions and the only distinction is where are the black and where white balls are.

We can choose the position of black balls in $\binom{n}{r}$ ways, therefore, white ones are on the remaining positions.

Using binomial we can have explanation written below:

The balls can be arranged in n! possible permutations.

To be precise one particular arrangement includes $r!(n-r)!$ permutations. Since r black balls can be permuted in r! ways and white balls in (n-r)! different orders.

So basically it yields,

$r! \times (n-r)!$ permutations.

So the actual amount is,

$\frac{r!}{(n-r)!}= \binom{n}{r}=\binom{n}{n-r}$

6 0

4 years ago

A regular hexagon has a perimeter of 70 m. Find its area. Leave your answer in simplest radical form.

Semmy [17]

A HEXA=6, gon, has 6 sides, and we know the perimeter, all sides added up, is 70, so one side is just 70/6, or 35/3

$\bf \textit{area of a polygon}\\\\
A=\cfrac{1}{4}ns^2\ cot\left( \frac{180}{n} \right)\qquad 
\begin{cases}
n=\textit{number of sides}\\
s=\textit{length of one side}\\
\frac{180}{n}=\textit{angle in degrees}\\
----------\\
n=6\\
s=\frac{35}{3}
\end{cases}
\\\\\\
A=\cfrac{1}{4}\cdot 6\cdot \left( \frac{35}{3} \right)^2\cdot ot\left( \frac{180}{6} \right)$

6 0

4 years ago

Suppose y varies directly with x. If y = 12 when x = 4, find x when y = 24.

mash [69]

Answer:

x would equal 8.

Step-by-step explanation:

Since when y = 12, x = 8, when y is 24, it is multiplied by 2. Multiple the x by 2 and it would be 8.

5 0

2 years ago

2. A geological study indicates that an exploratory oil well drilled in a particular region should strike oil with probability 0

yKpoI14uk [10]

Answer:

3.07% probability that the third oil strike comes on the fifth well drilled.

Step-by-step explanation:

For each oil drill, there are only two possible outcomes. Either there is a strike, or there is not. The probability that oil is striken in a trial is independent of other trials. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

Strike oil with probability 0.20.

This means that $p = 0.2$

Find the probability that the third oil strike comes on the fifth well drilled.

2 strikes on the first four drills(P(X = 2) when n = 4) and strike on the fifth(0.2 probability).

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 2) = C_{4,2}.(0.2)^{2}.(0.8)^{2} = 0.1536$

0.2*0.1536 = 0.0307

3.07% probability that the third oil strike comes on the fifth well drilled.

8 0

3 years ago

Veronica’s velocity was measured as 4.3 m/s. She displaced 20 meters in 4.7 seconds. Which piece of information is missing for t

Anit [1.1K]

Answer:

Direction is missing

Step-by-step explanation:

Veronica’s velocity was measured as 4.3 m/s. She displaced 20 meters in 4.7 seconds. We know that velocity is a vector quantity. It has both magnitude as well as direction. Velocity is defined as the total distance per unit time I.e.

i.e. the magnitude of velocity is 4.3 m/s

Here, only velocity is given but its direction is missing. So, the missing information is " the direction ".

5 0

3 years ago

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