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.

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