Roll a die 10 sided die 3 times. what is the probability that the sequence is strictly increasing or decreasing?

The probability of obtaining a sequence which is neither strictly increasing nor decreasing in 0.76.

Step-by-step explanation:

We have 10 possible outcomes on a single throw.

So, outcomes in 3 throws = outcomes.

Let x be the number of strictly increasing arrangements.

Let y be the number of strictly decreasing arrangements.

Let z be the number of outcomes that are neither strictly decreasing nor strictly increasing

So, we have

If we look at a strictly increasing arrangement from the other/opposite side, it will look like a strictly decreasing arrangement.

So, x = y

Hence, we can say the final equation will be :

And for strictly increasing arrangements ,all 3 numbers will be different and it can be done in 10C3 ways.

10C3= = 120 ways

So,

Thus

So, the probability is =

Therefore, the probability of obtaining a sequence which is neither strictly increasing nor decreasing in 0.76.

312312

step-by-step explanation:

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.