A bowl of candy contains many pieces of candy but only six different types of candy. How many ways can three pieces of candy be removed from the bowl? Assume you can remove one or more pieces of the same type of candy.
all the same color: 6 ways
two the same color: 6*5=30 ways
all different colors: 6*5*4=120 ways
To find the number of ways to remove three pieces of candy from the bowl, we can use the concept of combinations.
First, we need to determine the number of choices for each piece of candy. Since there are six different types of candy in the bowl, there are six options for the first piece, six options for the second piece, and six options for the third piece.
To calculate the total number of ways to choose the candy pieces, we need to multiply the number of choices for each piece together:
6 options for the first piece * 6 options for the second piece * 6 options for the third piece = 6 * 6 * 6 = 216.
Therefore, there are 216 ways to remove three pieces of candy from the bowl.