If you have 10 bottles of milk that are all different kinds,and you have 10 hous

Question

If you have 10 bottles of milk that are all different kinds,and you have 10 houses to delivery them to. How many ways canyou deliver them? Not every house has to have a bottle ofmilk. That is the part the confused me on how to do thisproblem. I am not sure how to calculate it since you can have10 bottles to one house nad none to another, 9 bottles to one house1 bottle to another and none to the rest, etc.. Any help would be apprectiatied! If you have 10 bottles of milk that are all different kinds,and you have 10 houses to delivery them to. How many ways canyou deliver them? Not every house has to have a bottle ofmilk. That is the part the confused me on how to do thisproblem. I am not sure how to calculate it since you can have10 bottles to one house nad none to another, 9 bottles to one house1 bottle to another and none to the rest, etc.. Any help would be apprectiatied!

Explanation / Answer

You have 10 bottles and 10 houses. In order to distribute thebottles over the houses, pick the first bottle and deliver it toone of the houses; there are 10 possibilities. Then pick the secondbottle and deliver it to one of the houses. Since you can delivermore than one bottle to a house, there are still 10 possibilitiesleft. Then pick the third one, and continue the same way, and soon. This method of reasoning yields that there are 10^10 possibleways to deliver the bottles. More general, it would be {#houses}^{# bottles}. Hope this helps!

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.