Mathematics, 23.07.2019 16:00 jsdlfjlk1936

In how many ways can 2 red, 2 black, 3 white and 2 blue balls be selected from 4 red, 3 black, 4 white and 8 blue balls? in how many ways can they be arranged?

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Answer from: garretthyatt123

The ways of arrangement of the balls are illustrations of combinations.

The number of selection is 2016

The given parameters are:

Total number of balls

$\mathbf{Blue = 8}$

$\mathbf{White = 4}$

$\mathbf{Black = 3}$

$\mathbf{Red = 4}$

Selected balls

$\mathbf{Blue = 2}$

$\mathbf{White = 3}$

$\mathbf{Black = 2}$

$\mathbf{Red = 2}$

So, the number of selection is:

$\mathbf{n =^8C_2 \times ^4C_3 \times ^3C_2 \times ^4C_2}$

Apply combination formula, we have:

$\mathbf{n =28 \times 4 \times3 \times 6}$

$\mathbf{n =2016}$

Hence, the number of selection is 2016

Read more about combinations at:

link

Answer from: DeathFightervx

From the total pool of colored balls, one can choose 2 reds, 2 blacks, 3 whites, and 2 blues in

$\dbinom42\cdot\dbinom32\cdot\dbinom43\cdot\dbinom82=6\cdot3\cdot4\cdot28=2016$

ways.

I'm assuming no ball of the same color is distinguishable from any other ball of the same color. So when I'm considering the possible arrangements, if I had lined up the ball as

red1 - black - red2 - ...

then this would be no different that

red2 - black - red1 - ...

So I now have 9 balls to arrange, which means there are 9!=362,880

total possible permutations of them. But order among distinct colors is assumed to not matter. This means I have to divide the total number of permutations by the number of ways I could permute balls of the same color. Then there would be a total of

$\dfrac{9!}{2!\cdot2!\cdot3!\cdot2!}=7,560$

ways of arranging the balls I had selected.

Answer from: Quest

(0,,,0)

step-by-step explanation:

the table of x and y values is shown in the attached pic(part of question)

we have to decide according that graph

given points are (0, 0) (–1, 0), (2, 0)

when we graph these points on graph they show an increasing line as shown in the attached pic

Answer from: Quest

Hello!

the answer is:

the correct option:

b. $x=2.23$

why?

to solve the problem, we need to remember how to operate to simplify exponential expressions using the logarithms.

we are given the equation:

$7^{x}=77$

then, using placing logarith with base 7 on both sides of the equation, we have:

$7^{x}=77log_{7}(7^{x})=log_{7}(77)x=log_{7}(77)x=2.2322$

so, rounding the obtained result to two decimal places (nearest hundreth), we have:

$x=2.23$

hence, we have that the correct option:

b. $x=2.23$

have a nice day!

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In how many ways can 2 red, 2 black, 3 white and 2 blue balls be selected from 4 red, 3 black, 4 whi...