A box contains 20 different balls numbered from 1 to 20 (different balls have different numbers). At each step, we select a ball uniformly at random, record the number on it, and put it back in the box. This experiment is repeated 10 times. Find the probability that all the numbers recorded were distinct.

P = 0.0655

Step-by-step explanation:

First, we are going to calculate the number of ways in which we can select the 10 balls. This is calculated using the rule of multiplication as:

Because we have 20 different balls every time and the experiment is repeated 10 times.

Then, from that ways, there are C ways where all the numbers recorded are distinct. It is calculated as:

Because, the first time, we have 20 options, the second time, we can just select 19 balls because we can not repeat the numbers, the third time, we can just select 18 balls and we need to keep doing this until get to the 10th time.

Finally, the probability that all the numbers recorded were distinct is calculated as C/T and it is equal to:

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!