- #1
YusifNurizade
- 6
- 0
Hello all,
My name is Yusif Nurizade; long time lurker, first time poster.
I am taking a summer class which is going at a rather quick pace and I could really use some help with the following problem:
A total of 11 different gifts are to be distributed among 15 children. How many different ways are there to distribute the gifts if (a) A child can receive any number of gifts. (b) each child can receive at most one gift.
I've confirmed the answer for part b to be 15C11 * 11!
The answer I came up with for part a is 15C11 * 12^11. I initially suspected a to have a greater number of choices than b because it encompasses the latter. My reasoning is that either child can have any number of gifts, including none, ergo 12 possible gifts scenarios per 11 children. I am, however, unsure of my answer and my mind keeps wandering asking whether I've considered some of the children getting less because one of them got a certain number.
I would really appreciate any help you could provide, particularly how I could arrive at the answer rather than the answer itself because it is really much more important that I understand the method.
Looking forward to your replies on what I am sure is the first of many posts.
Yusif Nurizade
My name is Yusif Nurizade; long time lurker, first time poster.
I am taking a summer class which is going at a rather quick pace and I could really use some help with the following problem:
A total of 11 different gifts are to be distributed among 15 children. How many different ways are there to distribute the gifts if (a) A child can receive any number of gifts. (b) each child can receive at most one gift.
I've confirmed the answer for part b to be 15C11 * 11!
The answer I came up with for part a is 15C11 * 12^11. I initially suspected a to have a greater number of choices than b because it encompasses the latter. My reasoning is that either child can have any number of gifts, including none, ergo 12 possible gifts scenarios per 11 children. I am, however, unsure of my answer and my mind keeps wandering asking whether I've considered some of the children getting less because one of them got a certain number.
I would really appreciate any help you could provide, particularly how I could arrive at the answer rather than the answer itself because it is really much more important that I understand the method.
Looking forward to your replies on what I am sure is the first of many posts.
Yusif Nurizade