Probability Calculation:

To calculate the probability that 3 particular mathematics books will be together, we need to determine the total number of possible arrangements and the number of favorable arrangements.

Total Number of Arrangements:

There are 10 books on the shelf, so the total number of arrangements can be calculated using the formula for permutations. Since the order of the books matters, we use the formula for permutations:

nPr = n! / (n-r)!

where n is the total number of books and r is the number of books we are selecting.

In this case, n = 10 (6 mathematics books + 4 physics books) and r = 3 (since we want 3 particular mathematics books to be together).

So, the total number of arrangements is:

10P3 = 10! / (10-3)! = 10! / 7! = 10 * 9 * 8 = 720

Favorable Arrangements:

Now, we need to determine the number of favorable arrangements where the 3 particular mathematics books are together. Since the 3 books need to be together, we can consider them as a single entity.

So, we have 8 entities (1 group of 3 mathematics books, 4 physics books, and 1 group of 3 remaining mathematics books).

Now, the total number of arrangements of these 8 entities can be calculated using the formula for permutations:

8P8 = 8! / (8-8)! = 8! / 0! = 8!

And within the group of 3 remaining mathematics books, they can be arranged among themselves in 3! ways.

Therefore, the total number of favorable arrangements is:

8! * 3! = 40,320

Probability Calculation:

The probability is given by the ratio of the number of favorable arrangements to the total number of arrangements:

Probability = (Number of Favorable Arrangements) / (Total Number of Arrangements)

Probability = 40,320 / 720 = 56

Simplifying, we get:

Probability = 1 / 15

Therefore, the probability that 3 particular mathematics books will be together is 1/15, which corresponds to option A.