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Mathematics

1 answer:

Vedmedyk [2.9K]3 years ago

5 0

Answer:

with what?

Step-by-step explanation:

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Suppose we want to choose 5 colors, without replacement, from 8 distinct colors.1. If the order is relevant, how many can be don

Charra [1.4K]

(1) From the information given, if we want to choose 5 colors from 8 distinct colors and the order in which the selection is made is relevant, then what we have is a permutation.

The formula is given as;

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

This formula means we need to select/arrange r items out of a total of n items and the anwer derived would be the total number of arrangements possible.

Therefore, we would have;

$\begin{gathered} nP_r\Rightarrow_8P_5 \\ _8P_5=\frac{8!}{(8-5)!}\Rightarrow\frac{8!}{3!} \\ _8P_5=\frac{8\times7\times6\times\ldots1}{3\times2\times1}\Rightarrow\frac{40320}{6} \\ _8P_5=6720 \end{gathered}$

Therefore, if the order is relevant, this selection can be done in 6,720 ways.

(2) If the order is NOT relevant, then what we need to calculate is a combination and the formula is;

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

The formula can now be applied as follows;

$\begin{gathered} _nC_r\Rightarrow_8C_5 \\ _8C_5=\frac{8!}{(8-5)!\times5!} \\ _8C_5=\frac{8!}{3!\times5!}\Rightarrow\frac{8\times7\times6\times\ldots1}{(3\times2\times1)\times(5\times4\times\ldots1)} \\ _8C_5=\frac{40320}{6\times120} \\ _8C_5=56 \end{gathered}$

If the order is not relevant, then the selection can be done in 56 ways.

3 0

1 year ago

The graph of the w=equation x+3y=6 intersects the y axis at the point whose coordinate are

nevsk [136]

Y intercept = when x = 0
Plug in x = 0
0 + 3y = 6
3y = 6, y = 2

Solution: a, (0,2)

8 0

3 years ago

Eliminate the parameter. x = t2 + 2, y = t2 - 4

stepan [7]

$\bf \begin{cases}
x=t^2+2\implies x-2=t^2\implies \sqrt{x-2}=\boxed{t}\\\\
y=t^2-4\\
----------\\
y=\left( \boxed{\sqrt{x-2}} \right)^2-4\implies y=x-2-4\\\\
y=x-6
\end{cases}$

just a plain vanilla substitution

8 0

3 years ago

Read 2 more answers

A circle with radius r is inscribed into a right triangle. Find the perimeter of the triangle if the length of the hypotenuse is

tankabanditka [31]

Answer: 56

Step-by-step explanation:

4=(a+b-24)/2

32=a+b

32+24=56

5 0

3 years ago