Final answer:
To find the number of different groups of 12 that can be formed from 17 volunteers, we can use the combination formula. The number of combinations of n objects taken r at a time is given by nCr = n! / (r!(n-r)!). Substituting the values and simplifying gives us 6188 different groups of 12.
Step-by-step explanation:
To find the number of different groups of 12 that can be formed from 17 volunteers, we can use the combination formula. The number of combinations of n objects taken r at a time is given by the formula:
nCr = n! / (r!(n-r)!)
Substituting the values, we have:
17C12 = 17! / (12!(17-12)!)
17C12 = 17! / (12! * 5!)
Now, calculate the factorial values and simplify:
17C12 = (17 * 16 * 15 * 14 * 13) / (12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1)
17C12 = 6188
Therefore, there are 6188 different groups of 12 that can be formed from 17 volunteers.