Counting problem

[rajatvmittal]

In how many ways 5 rings of different types can be worn in 4 fingers?

is it 4^5 or 5^4?

Also, In how many ways 7 pictures can be hung from 5 picture nails on a wall?

Please explain both the problems using of Slot method?

[abhi.iitb]

Solution for the below problem is here:

since in the mentioned problem there is no condition such as every finger has to have at least 1 ring so,
every ring has 4 choices- 4 ways( it can be worn in any one of four fingers)
considering we have 5 rings so total no of ways in which 5 rings can be worn in four fingers -4x4x4x4x4 that is 4^5.

I hope it is well understood...


solution for the 7 picture problem:

Since using basic logic we can assume that on 1 nail we can hung only 1 picture. So,

1st nail has 7 picture choices- 7 ways
2nd nail has 6 choices since 1 picture is already hung on 1st nail- 6 ways
.
.
.
.
5th nail has 3 choices since 4 pictures are already hung on 4 nails-3 ways

multiplying all these possibilities- 7x6x5x4x3
we get total no of ways in which all these pictures can be hung-2520 ways.

what exactly is this slot method???

[rajatvmittal]

Hi abhi

Thank you

could you please explain the first problem in detail with all the "such as" and how theses such as affect the answers.
such as - as every finger has to have at least 1 ring or at most one ring...

Thanks
Rajat