In the permutations of n things r, taken together, the number of permutations in which m particular things occur together is `""^(n-m)P_(r-m)xx""^(r)P_(m)`.

Answer

To solve the problem, we need to find the number of permutations of n things taken r at a time, where m particular things are required to occur together. Here’s the step-by-step solution:

### Step 1: Understand the Problem
We have n distinct items and we want to select r items from these n items. Among these r items, we want m particular items to be together.

### Step 2: Treat m Particular Items as One Unit
Since m particular items need to be together, we can treat these m items as a single unit or block. Therefore, instead of m items, we now have 1 block of m items.

### Step 3: Calculate the New Total
Now, the total number of items we consider is:
- The block of m items (1 unit)
- The remaining n - m items

Thus, the total number of units (blocks) we have is:
\[ (n - m) + 1 = n - m + 1 \]

### Step 4: Determine the Number of Permutations
Now we need to select r items from these \( n - m + 1 \) units. The number of ways to choose \( r - m + 1 \) units from \( n - m + 1 \) is given by:
\[ ^{(n - m + 1)}C_{(r - m + 1)} \]

### Step 5: Arrange the m Items Within Their Block
The m particular items can be arranged among themselves in \( m! \) ways.

### Step 6: Combine the Results
Thus, the total number of permutations where m particular items are together is given by:
\[ ^{(n - m + 1)}P_{(r - m + 1)} \times m! \]

### Step 7: Final Expression
The expression can be rewritten using the permutation formula:
\[ ^{(n - m)}P_{(r - m)} \times ^{(r)}P_{(m)} \]

### Conclusion
Thus, the final result is:
\[ ^{(n - m)}P_{(r - m)} \times ^{(r)}P_{(m)} \]