There are 20 identical printing jobs to be sent to 5 different printers. (a) one of the printers is much faster than the other four. how many ways are there to distribute the jobs if the faster printer gets at least 7 jobs? (b) 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)

a) 482,718,652,416,000

b) 80,453,108,736,000

Step-by-step explanation:

(a)

There are (combinations of 20 taken 7 at a time)

different ways of sending 7 jobs to the fastest printer.

There are

13! = 6,227,020,800

ways of sending the other 13 jobs to the rest of the printers (assuming that none of the printers is idle)

By the Fundamental Rule of counting, there are  

77520*6,227,020,800 = 482,718,652,416,000

different ways of distributing the jobs with the faster printer getting at least 7 jobs.

(b)

There are (combinations of 20 taken 7 at a time)

different ways of sending 7 jobs to the fastest printer.

There are (combinations of 13 taken 3 at a time)

different ways of sending 3 jobs to the printer that is almost out of paper.

There are  

10! = 3,628,800

different ways of sending the 10 remaining jobs to the rest of the printers.

By the Fundamental Rule of counting, there are  

77,520*286*3,628,800 = 80,453,108,736,000

different ways to distribute the jobs so that the printer that is almost out of paper does not get more than three jobs and the faster one gets at least 7 jobs.

the most boring ever written

step-by-step explanation:

i am writing something. yes, i plan to make it the most boring thing ever written. i go to the store. a car is parked. many cars are parked or moving. some are blue. some are tan. they have windows. in the store, there are items for sale. these include such things as soap, detergent, magazines, and lettuce. you can enhance your life with these products. soap can be used for bathing, be it in a bathtub or in a shower. apply the soap to your body and rinse. detergent is used to wash clothes. place your dirty clothes into a washing machine and add some detergent as directed on the box. select the appropriate settings on your washing machine and you should be ready to begin. magazines are stapled reading material made with glossy paper, and they cover a wide variety of topics, ranging from news and politics to business and stock market information. some magazines are concerned with more recreational topics, like sports card collecting or different kinds of hairstyles. lettuce is a vegetable.