Let’s count – Distribution of objects, 2

Do your best in trying to solve the following problems. It is normal that this step will take some time, we recommend to perseverate and wait before looking at the complete solution of the exercises in the video or in the pdf below.

Exercise 3.

The set (mathcal P(I_n)) of parts of (I_n) is the set of all subsets of (I_n).
1. Describe (mathcal P(I_2)).
2. Describe a 1-to-1 map between (mathcal P(I_n)) and the 2-sharings of (I_n).
3. Describe a 1-to-1 map between (mathcal P(I_n)) and the (n)-sequences of ({0,1}).

Exercise 4

Describe the 2-collections of I₃ and the corresponding 3-compositions of 2.