You have 10 candies, 2 of which are identical. You want to eat one afterbreakfast, one after lunch, and one after dinner (childish I know...)Assume that this order of eating the candies is important. In howmany ways can you eat 3 candies? Hint: Solve this using these steps:• First, count the possibilities in which all candies are different (sowork with 9 candies).• Then, count the possibilities in which 2 of the candies are identi-cal.• Finally, add them up.

Sure, let's solve this step by step:

1. First, we count the possibilities in which all candies are different. So, we work with 9 candies. The number of ways to choose 3 candies out of 9 is given by the permutation formula P(n,r) = n! / (n-r)!. Here, n is the total number of candies (9) and r is the number of candies we want to choose (3). So, P(9,3) = 9! / (9-3)! = 987 = 504 ways.

2. Next, we count the possibilities in which 2 of the candies are identical. So, we work with 8 different candies and 1 pair of identical candies. We have 3 scenarios here: a) The identical candies are eaten at different times. This can happen in 32 = 6 ways. And the third candy can be any of the remaining 8 candies. So, we have 68 = 48 ways. b) The identical candies are eaten consecutively. This can happen in 23 = 6 ways. And the third candy can be any of the remaining 8 candies. So, we have 68 = 48 ways. c) The identical candies are eaten first and last. This can happen in 2 ways. And the third candy can be any of the remaining 8 candies. So, we have 2*8 = 16 ways. Adding these up, we get 48 + 48 + 16 = 112 ways.

3. Finally, we add up the possibilities from step 1 and step 2. So, the total number of ways to eat 3 candies is 504 + 112 = 616 ways.