To solve this question, the user needs to understand the concept of permutations. Permutations refer to the different ways a set of objects can be arranged in a particular order.

In this case, there are ten people, and the photographer wants to take pictures of all possible groupings. To find the number of pictures the photographer will take, we need to calculate the number of permutations of ten people taken at a time.

Now, and the user has to know how to calculate permutations.

Now let's go through each option and explain why it is right or wrong:

A. 100: This option is incorrect because it represents a simple multiplication of 10 (the number of people) by 10 (the number of positions the photographer can place them). However, this calculation does not account for the different arrangements and orderings that can be produced by shuffling the group.

B. 10 to the power 10: This option is incorrect because it represents the total number of possible arrangements when there are 10 choices for each of the 10 positions. However, this would be true if the photographer was arranging the group in a fixed order repeatedly, rather than shuffling them for each picture.

C. 362880: This option is incorrect because it represents the factorial of 10 (i.e., 10!), which is the total number of possible arrangements of 10 distinct objects in a fixed order. However, the question asks for the number of pictures taken when the group is shuffled, not arranged in a fixed order.

D. 3628800: This option is correct because it represents the total number of different pictures the photographer will take when shuffling the group of ten people. It is calculated by multiplying the number of choices for the first position (10) by the number of choices for the second position (9) by the number of choices for the third position (8), and so on, until there is one choice left for the last position (1). This can be written as 10 x 9 x 8 x ... x 1 = 10!.

Therefore, the correct answer is option D: 3628800.