Answer:
[tex]C(99,55)\,C(33,22)\,C(44,33)[/tex]
Step-by-step explanation:
A permutation refers to arrangement of the objects or numbers in order. Combinations refers to selecting the objects or numbers from a group of objects or collection such that the order of the objects does not matter.
A delegation of 55 Republicans, 22 Democrats, and 33 Independents is selected from a group of 99 Republicans, 33 Democrats, and 44 Independents.
So,
Number of ways [tex]=C(99,55)\,C(33,22)\,C(44,33)[/tex]