There are 17 appetizers available at a restaurant. from these, barbara is to choose 12 for her party. how many groups of 12 appetizers are possible?

This is a question of combination. In other words, the question requires determination of number of ways in which 12 appetizers can be chosen form a total of 17 appetizers.

Therefore,
Possible number of 12 groups = 17C12 = 17!/[12!*(17-12)!] = 6188

Best answer that i found on yahoo ok   set :   x= length of 2nd piece in cm  x- 3= length of 1st piece in cm  x-4= length of 3rd piece in cm  then since you know they all came from the 20 cm ribbon you add them together and set them equal to 20x+ x-3 +x-4 = 20  3x - 7= 20  3x= 27  x= 9  the shortest piece is the third piece which is x- 4  x-4  9-4 = 5  the length of the smallest piece is 5 cm.  the other lengths are  9 cm  6 cm