A croissant shop has plain croissants, cherry croissants, chocolate croissants, almond croissants, apple croissants, and broccoli croissants.

We need to find the number of way to choose 6 dozen croissants.

Formula: The number of r-combinations with repetition allowed that can be selected from a set of n elements is

(r+n-1 r)

This equals the number of ways r objects can be selected from n categories of objects with repetition allowed.

Using this above formula, the number of ways to choose 6 dozen croissants is given by:

\(\displaystyle{\left({r}+{n}-{1}{r}\right)}={\left({6}+{72}-{1}{72}\right)}={\left({77}{72}\right)}=\frac{{{\left({77}\right)}!}}{{{\left({72}\right)}!\cdot{5}!}}=\frac{{{77}\cdot{76}\cdot{75}\cdot{74}\cdot{73}\cdot{\left({72}\right)}!}}{{120}}={19757815}\)

Therefore, the number of ways to choose 6 dozen croissants is 19757815.

We need to find the number of way to choose 6 dozen croissants.

Formula: The number of r-combinations with repetition allowed that can be selected from a set of n elements is

(r+n-1 r)

This equals the number of ways r objects can be selected from n categories of objects with repetition allowed.

Using this above formula, the number of ways to choose 6 dozen croissants is given by:

\(\displaystyle{\left({r}+{n}-{1}{r}\right)}={\left({6}+{72}-{1}{72}\right)}={\left({77}{72}\right)}=\frac{{{\left({77}\right)}!}}{{{\left({72}\right)}!\cdot{5}!}}=\frac{{{77}\cdot{76}\cdot{75}\cdot{74}\cdot{73}\cdot{\left({72}\right)}!}}{{120}}={19757815}\)

Therefore, the number of ways to choose 6 dozen croissants is 19757815.