Problem Solving

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?

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???

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