The number of ways to choose 7 volunteers out of 13 can be calculated using the combination formula, which is:
nCr = n! / r!(n-r)!
Where n is the total number of volunteers (13) and r is the number of volunteers needed (7).
Using this formula, we get:
13C7 = 13! / 7!(13-7)!
= (13 x 12 x 11 x 10 x 9 x 8 x 7!) / (7 x 6 x 5 x 4 x 3 x 2 x 1 x 6!)
= (13 x 12 x 11 x 10 x 9 x 8) / (7 x 6 x 5 x 4 x 3 x 2 x 1)
= 1,171,856
Therefore, there are 1,171,856 different groups of 7 volunteers that can be formed from the 13 volunteers.