20 identical printing jobs are sent to 5 different printers. One of the printers is almost out of paper. How many ways are there to distribute the jobs so that the printer that is almost out of paper does not get more than three jobs? (In addition to the fact that the faster one gets at least 7 jobs.)

Aswimming pool has an input pump for filling the pool and an output pump for emptying the pool. the input pump can fill the pool in 3 hours, and the output pump can drain the pool in 5 hours. as you go to bed, the pool is full, but a neighbor’s kid turns on the output pump. at midnight, you awake to find the pool half empty. immediately, you turn on the input pump, but you are sleepy and forget to turn off the output pump. at what time will the pool become full?

Ateacher brought a pack of 17 batteries . each calculator uses 3 batteries . how many calculator can the teacher fill with batteries

Events a and b are independent. the probability of a occurring is 2/5. the probability of b occurring is 1/4. what is p(a and b)?