you play a CD with 11 songs using the shuffle settings. find the probability that the CD player plays song 3 first then song 5.

wouldn't that just be

(1/11)(1/10) or 1/110 ?

To find the probability that the CD player plays song 3 first and then song 5, we need to calculate the total number of possible outcomes and the number of favorable outcomes.

Here's how we can approach it:

1. Calculate the total number of possible outcomes:
Since there are 11 songs on the CD, the total number of possible outcomes is 11! (11 factorial). The "!" symbol denotes factorial, which means the product of all positive integers up to that number.

2. Calculate the number of favorable outcomes:
We need exactly two songs to be played, and the order should be song 3 first and then song 5. The remaining 9 songs can be played in any order. The number of ways to arrange these two specific songs is 2!.

3. Calculate the probability:
To calculate the probability, we divide the number of favorable outcomes by the total number of possible outcomes.

Probability = Number of favorable outcomes / Total number of possible outcomes.

Probability = (2! * 9!) / 11!

Now, let's compute the probability:

Number of favorable outcomes:
2! = 2 * 1 = 2

Total number of possible outcomes:
11! = 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1

Probability = (2 * 9!) / 11!

At this point, we can calculate the probability using a calculator or simplifying the equation further.

Note: The factorial notation means multiplying a sequence of consecutive positive integers. For large numbers like 11!, the exact calculation might be computationally intensive. In such cases, you can use scientific calculators or programming languages like Python to compute it accurately.