What is the value ofnpna)zerob)n!c)nd)1Correct answer is option 'B'. C...
**Explanation:**
To find the value of `npn`, we need to understand the concept of permutations.
**Permutations:**
In mathematics, permutations refer to the arrangement of objects in a particular order. The number of permutations of n objects taken all at a time is denoted by `nPn` or `n!` (read as n factorial).
**Factorial:**
Factorial is a mathematical operation that represents the product of all positive integers from 1 to a given number. It is denoted by the symbol `!`. For example, `5!` (read as 5 factorial) is equal to 5 × 4 × 3 × 2 × 1 = 120.
**Value of nPn:**
When we calculate `nPn`, it means we want to arrange n objects taken all at a time in a particular order. In other words, we want to find the number of ways in which n objects can be arranged without repetition.
Let's take an example to understand this. Suppose we have 4 objects: A, B, C, D. We want to find the number of ways in which these objects can be arranged without repetition.
The possible arrangements are:
ABCD, ABDC, ACBD, ACDB, ADBC, ADCB, BACD, BADC, BCAD, BCDA, BDAC, BDCA, CABD, CADB, CBAD, CBDA, CDAB, CDBA, DABC, DACB, DBAC, DBCA, DCAB, DCBA
As we can see, there are 24 possible arrangements, which is equal to 4!.
Therefore, the value of `npn` is `n!`. Hence, the correct answer is option 'B' - `n!`.