Permutations!!

1 answer:

3 0

Since the problem specifically stated that the people gather around the table, therefore we assume a circular table hence a circular formation of gathering. Since the arrangement is important therefore we use the permutation.

nPr = n! / (n – r)!

However before we proceed with our calculation we MUST first affix a reference point since the formation is circle. Imagine that the reference point is the 1st point made when you draw a circle, so it is the both the 0 degrees and the 360 degrees.

Let us say that one of the actors is the reference point. So there are now only 8 actors which places can be interchanged. Since all actors have to sit together, hence the arrangements are:

8P8 = 8! / (8 – 8)! = 40,320

Now since there are 13 total people, therefore the arrangements of the other 4 people are:

4P4 = 4! / (4 – 4)! = 24

We multiply all to get the total number of arrangements:

Total arrangements = 40320 * 24 * 1 (1 is the reference point)

Total arrangements = 967,680

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Lesechka [4]

Answer:

$\displaystyle x = 2 \sqrt{3}$

Step-by-step explanation:

we would like to solve the following equation:

$\displaystyle \sqrt{3} = \frac{6}{x}$

in order to do so do cross multiplication:

$\displaystyle x \sqrt{3} = 6$

divide both sides by √3:

$\displaystyle x = \frac{6}{ \sqrt{3}}$

since we ended up with a square root on the denominator so we can consider rationalising the denominator to do so multiply both numerator and denominator by √3 which yields:

$\displaystyle x = \frac{6}{ \sqrt{3}} \times \frac{ \sqrt{3} }{ \sqrt{ 3} }$