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dexar [7]
1 year ago
9

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

e?2. If it’s not relevant?
Mathematics
1 answer:
Charra [1.4K]1 year ago
3 0

(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.

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Time = 2\dfrac{1}{2}=2.5 years

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The principal value.

Solution:

Formula for amount is

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Putting the given values, we  get

34476=P\left(1+\dfrac{4}{100}\right)^{2.5}

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2 years ago
Miguel sells insurance. He earns a 6% commission on each sale he makes. Miguel has a goal of earning $600 in commissions. Miguel
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3 years ago
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Answer:

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Step-by-step explanation:

1. Compare the ratios 4 : 5 and 2 : 3.

Solution:

Express the given ratios as fraction

4 : 5 = 4/5 and 2 : 3 =2/3

Now find the L.C.M (least common multiple) of 5 and 3

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Making the denominator of each fraction equal to 15, we have

4/5 = (4 ×3)/(5 ×3) = 12/15 and 2/3 = (2 ×5)/(3 ×5) = 10/15

Clearly, 12 > 10

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Solution:

Express the given ratios as fraction

5 : 6 = 5/6 and 7 : 9 =7/9

Now find the L.C.M (least common multiple) of 6 and 9

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Making the denominator of each fraction equal to 18, we have

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Now, 25/50 > 24/50

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