What is an explicit formula for the geometric sequence 64,16,4,1,... where the first term
1 answer:
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Answer:
a) 369,600
b) 0.0000649
Step-by-step explanation:
If all of the A's, B's, C's and D's were different, the number of ways to form a molecule would be calculated as n!. However, given that every molecule is repeat 3 times, we need to reduce the number dividing by 3! for every type of molecule.
It means that the number of ways in which we can organize n elements where not all of them are equal is calculated as:
Where k is the number of elements that are differents and are the number of times that every element appears.
Now, we have 4 different types of molecules (A,B,C,D) so k is equal to 4. Additionally, there are 3 molecules of type A, 3 of type B, 3 of type C, and 3 of type D, so and
. It means that there are 369,600 ways to form chain molecules and it is calculated as:
Now, the number of ways where all three molecules of each type end up next to one another is calculated as:
Because, first we have 4 possible types of molecules to occupy the first three positions, then we have 3 possible types of molecules to occupy the following 3 positions, then we have 2 possible types of molecules and finally we have 1 possible type of molecule
So, the probability that all three molecules of each type end up next to one another is calculated as: