Answer:
The value is ![P(X = 8) = 0.64](https://tex.z-dn.net/?f=P%28X%20%3D%208%29%20%3D%200.64%20)
Step-by-step explanation:
From the question we are told that
The number of recognized colors is n = 12
The number of teams is k = 8
Generally the total number of color pairs available to be selected is mathematically represented as
![N = ^{12} C_2](https://tex.z-dn.net/?f=N%20%3D%20%20%5E%7B12%7D%20C_2)
Here C stands for combination
=> ![N = 66](https://tex.z-dn.net/?f=N%20%3D%20%2066%20)
Generally the number of ways of selecting color pairs so that no two teams will have chosen the same pair of color is mathematically represented as
![P(8) = \ ^{N} P_8](https://tex.z-dn.net/?f=P%288%29%20%3D%20%20%5C%20%5E%7BN%7D%20P_8)
![P(8) = \ ^{66} P_8](https://tex.z-dn.net/?f=P%288%29%20%3D%20%20%5C%20%5E%7B66%7D%20P_8)
Here P stands for permutation
![P(8) =231580827878400](https://tex.z-dn.net/?f=P%288%29%20%3D231580827878400%20)
Generally the total number of way the teams can select a pair of color is mathematically represented as
![P = (N)^8](https://tex.z-dn.net/?f=P%20%3D%20%28N%29%5E8)
=> ![P = (66)^8](https://tex.z-dn.net/?f=P%20%3D%20%2866%29%5E8)
=> ![P = 3.6004061*10^{14}](https://tex.z-dn.net/?f=P%20%3D%203.6004061%2A10%5E%7B14%7D)
Generally the the probability that no two teams will have chosen the same pair of color is mathematically represented as
![P(X = 8) = \frac{231580827878400}{3.6004061*10^{14}}](https://tex.z-dn.net/?f=P%28X%20%3D%208%29%20%3D%20%20%5Cfrac%7B231580827878400%7D%7B3.6004061%2A10%5E%7B14%7D%7D)
=> ![P(X = 8) = 0.64](https://tex.z-dn.net/?f=P%28X%20%3D%208%29%20%3D%200.64%20)
2 because you need the fírmala and divided
<h3>The common ratio of the sequence is -3</h3>
<em><u>Solution:</u></em>
<em><u>Given sequence is:</u></em>
-2, 6, -18, 54
We have to find the common ratio of sequence
Common ratio is the ratio between two consecutive numbers in the sequence
<em><u>Find the ratio of a term to its previous term</u></em>
![r = \frac{6}{-2} = -3\\\\r = \frac{-18}{6} = -3\\\\r = \frac{54}{-18} = -3](https://tex.z-dn.net/?f=r%20%3D%20%5Cfrac%7B6%7D%7B-2%7D%20%3D%20-3%5C%5C%5C%5Cr%20%3D%20%5Cfrac%7B-18%7D%7B6%7D%20%3D%20-3%5C%5C%5C%5Cr%20%3D%20%5Cfrac%7B54%7D%7B-18%7D%20%3D%20-3)
Thus the common ratio of the sequence is -3
Set up a proportion
3 coins:8 notes and then the other one 24 coins : x (unknown notes)
they have a relationship so we can set them equal to each other.
3/8=24/x cross multiply: 8 * 24 = 192
Now divide that by 3: 192/3 = 64
So there are 64 notes in the bag