you play a CD that has 11 songs using the random setting find the probability that the CD player plays songs 3 first and then song 5.
no
To find the probability that the CD player plays song 3 first and then song 5 in a random setting, we need to calculate the total number of possible outcomes and the number of favorable outcomes.
The total number of possible outcomes can be found by calculating the number of ways the CD player can arrange the 11 songs. Since each song can be played only once, we can use the concept of permutations. The number of permutations of 11 songs taken all at once is denoted by 11!.
The number of favorable outcomes is 1. Since we are specifically looking for the order of song 3 first and then song 5, there is only one favorable outcome.
Therefore, the probability can be calculated as:
Probability = (Number of Favorable Outcomes) / (Total Number of Possible Outcomes)
Probability = 1 / 11!
To evaluate this, we can calculate the factorial of 11:
11! = 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 39,916,800
So the probability that the CD player plays song 3 first and then song 5 in a random setting is:
Probability = 1 / 39,916,800 ≈ 2.505×10^(-8)