If

then

The ODE in terms of these series is



We can solve the recurrence exactly by substitution:


So the ODE has solution

which you may recognize as the power series of the exponential function. Then

Answer:
18 : 10
4.5:2.5
27 : 15
Step-by-step explanation:
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Change the fractions so they have common denominators. For example. If adding 4/8 + 2/3, a common denominator of the two could be 24. Change both fractions to have a denominator of 24. To do this:
(4/8)×(3/3)= 12/24
(2/3)×(8/8)=16/24
Now that both fractions have denominators of 24, you can simply add the numerators to get your answer. in this case, it would be 28/24
When you're evaluating P(n, k), you are essentially saying there are n objects and you will need to arrange them in k spaces.
This is essentially the same as:

, which follows the formula:

If you're dividing by 4!, you are evaluating P(6, 2)