Two experiments are to be performed. the first can result in any one of m possible outcomes. if the first experiment results in outcome i, then the second experiment can result in any of ni possible outcomes, i = 1, 2, . . , m. what is the number of possible outcomes of the two experiments

The first experiment has M probabilities, and the second has I(m) outcomes, that depends on the result of the first.

And lets call m to the result of the first experiment.

If the outcome of the first experiment is 1, then the second experiment has 1 possible outcome.

If the outcome of the first experiment is 2, then the second experiment has 2 possibles outcomes.

If the outcome of the first experiment is M, then the second experiment has M possibles outcomes.

And so on.

So the total number of combinations C is the sum of all the cases, where we exami

1 outcome for m = 1

+

2 outcomes for m=2

+

.

.

.

+

M outcomes for m = M

C = 1 + 2 + 3 + 4 +...´+M

490*x + 700*y > 4000

It is < as it can be equal to 4000 per week or less than.