Final answer:
There are 45 different ways the child can take the 2 candy bars from the bucket of 10 different types of candy bars.
Step-by-step explanation:
The child is allowed to take 2 candy bars from a bucket of 10 different types of candy bars. To find the number of ways the child can take the 2 candy bars, we can use the concept of combinations. The formula for combinations is given by:
C(n, r) = n! / (r!(n-r)!)
Where n is the total number of items, r is the number of items being chosen. In this case, n = 10 and r = 2. Plugging in these values, we get:
C(10, 2) = 10! / (2!(10-2)!) = 10! / (2!8!) = (10 * 9) / (2 * 1) = 45
Therefore, there are 45 different ways the child can take the 2 candy bars from the bucket.