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# What is the number of possible permutations of 8 objects taken 3 at a time?

**Solution:**

Total permutation of n different things taken r at a time is given by \(^{n-1}P_{r-1}\)

We have to find a total permutation of 8 objects taken 3 at a time.

Here, n = 8 and r = 3

So, \(^{n-1}P_{r-1}\) = \(^{8-1}P_{3-1}\)

= \(^{7}P_{2}\)

= 7 × 6

= 42

Therefore, the number of possible permutations is 42.

Example: **What is the number of possible permutations of 6 objects taken 2 at a time?**

**Solution:**

Total permutation of n different things taken r at a time is given by \(^{n-1}P_{r-1}\)

We have to find a total permutation of 6 objects taken 2 at a time.

Here, n = 6 and r = 2

So, \(^{n-1}P_{r-1}\) = \(^{6-1}P_{2-1}\)

= \(^{5}P_{1}\)

= 5

Therefore, the number of possible permutations is 5.

## What is the number of possible permutations of 8 objects taken 3 at a time?

**Summary:**

The number of possible permutations of 8 objects taken 3 at a time is 42.

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