In a well-developed paragraph:

why was it a good idea to include all the races in the formation of the fellowship?

what advantages do each of the races potentially offer in the accomplishment of the goal?

There were many advantages of including all Middle-Earthian in the Fellowship. An important one was that none of the different races would get jealous, and tempers would rise. Also, having an Elf or Dwarf around could be helpful: Elves know magic and Dwarves are exemplary at smashing things (and at short distance sprinting). Each member has a different mindset, and that can help to form different plans that could be better than the original. Like I said earlier, having different people with different capabilities would be very useful. A Hobbit can sometimes do what a Man or a Wizard couldn't. For example, Frodo could carry the weight of the Ring while a Man would be affected and would turn against everyone and everything. Having all the races would also provide advantages in different territories. The territories would be more peaceful and open if one of their kind was in the Fellowship. The land wouldn't be (as) hostile to the group. Without each and every person in the Fellowship, the world of Middle-Earth surely would have fallen.