Answer :
If the cubes are labeled 1 through 9 and the first cube must be labeled 1, then there are 8 remaining cubes to arrange in ascending order from 2 to 9.
The probability of arranging the cubes in the correct order is the same as the probability of arranging the numbers 2 through 9 in ascending order. Since there is only one correct order out of the total possible orders, the probability is:
\[ \text{Probability} = \frac{1}{n!} \]
where \( n \) is the number of items to arrange. In this case, \( n = 8 \).
So, the probability is:
\[ \text{Probability} = \frac{1}{8!} \]
\[ \text{Probability} = \frac{1}{40320} \]
\[ \text{Probability} \approx 0.0000248 \]
Therefore, the probability that the rest of the cubes will be in order from least to greatest is approximately \( 0.0000248 \), or \( \frac{1}{40320} \).
Hope this helps!
The probability of arranging the cubes in the correct order is the same as the probability of arranging the numbers 2 through 9 in ascending order. Since there is only one correct order out of the total possible orders, the probability is:
\[ \text{Probability} = \frac{1}{n!} \]
where \( n \) is the number of items to arrange. In this case, \( n = 8 \).
So, the probability is:
\[ \text{Probability} = \frac{1}{8!} \]
\[ \text{Probability} = \frac{1}{40320} \]
\[ \text{Probability} \approx 0.0000248 \]
Therefore, the probability that the rest of the cubes will be in order from least to greatest is approximately \( 0.0000248 \), or \( \frac{1}{40320} \).
Hope this helps!
Answer:
- 1/5040
Step-by-step explanation:
To calculate the probability that the rest of the cubes will be in order from least to greatest after placing the first two cubes (labeled 1 and 2), we need to consider the total number of ways the remaining cubes can be arranged in ascending order.
Given that there are 7 cubes left (3 to 9) to be placed in order, the number of ways they can be arranged in ascending order is 1 (since there is only one way for them to be in order).
Therefore, the probability that the rest of the cubes will be in order from least to greatest is 1 out of the total possible arrangements of the remaining 7 cubes.
The total number of ways to arrange 7 distinct cubes is 7! (7 factorial), which is equal to 5040.
So, the probability is:
- 1/7! = 1/5040
- Q.E. :))
If u have questions feel free to ask
