A presidential candidate plans to begin her campaign by visiting the capitals of 5 of the 50 states. If the five capitals are randomly selected without replacement, what is the probability that the route is Sacramento, Albany, Juneau, Hartford, and Bismarck, in that order?

The probability is 1/254,251,200

Step-by-step explanation:

We proceed as follows;

Firstly, we are selecting 5 state capitals out of 50. The number of ways we can do this is 50P5 = 50!/5!(50-5)! = 254,251,200 ways

Now, out of this number of ways , only one route is desired in that particular order.

This means the probability of having the route scheduled in that particular order would be;

1/254,251,200

0.000000003933

Step-by-step explanation:

As the candidate will visit the capitals of 5 of the 50 states, the probability of each capital being selected is 1/50.

As we want a probability of 5 specific capitals in a specific order, we can calculate the probability of each capital being chosed:

First city being Sacramento: Probability of 1/50

Second city being Albany: Probability of 1/49 (as the first city is not available now)

Third city being Juneau: Probability of 1/48

Fourth city being Hartford: Probability of 1/47

Fifth city being Bismarck: Probability of 1/46

So the final probability is 1/(50*49*48*47*46) = 0.000000003933

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}

chicken chicken chicken

step-by-step explanation: