Concept: Permutation.np4 = 9 np3.n!/(n-4)! =9 n!/(n-3)!.1/(n-4)(n-3)! =9/(n-3)!.1/n-4 = 9.9n - 36 = 1.n = 37/9.I hope it will help u bt this is basic u should know.

Permutations and Combinations: nP3

Introduction:
In the field of mathematics, permutations and combinations are fundamental concepts that deal with the arrangement and selection of objects. Permutations refer to the arrangement of objects in a specific order, while combinations represent the selection of objects without considering the order.

Permutations:
Permutations are arrangements of objects in a particular order. The number of permutations of 'n' objects taken 'r' at a time is denoted by nPr or nPr. The formula to calculate permutations is:

nP3 = n! / (n-r)!

Where 'n' represents the total number of objects available, and 'r' represents the number of objects to be selected.

Calculation of nP3:
To find the value of nP3, we substitute the given values into the permutation formula and solve for the result.

Given: nP3 = 9

Let's substitute the values into the formula:

9P3 = 9! / (9-3)!
= 9! / 6!

Simplification of the Formula:
To simplify the formula, we need to calculate the factorial of the numbers involved. The factorial of a number is the product of all positive integers less than or equal to that number. For example, 5! (read as "5 factorial") is equal to 5 x 4 x 3 x 2 x 1.

Simplifying the formula further:

9! = 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
6! = 6 x 5 x 4 x 3 x 2 x 1

Substituting the calculated factorials back into the formula:

9P3 = (9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) / (6 x 5 x 4 x 3 x 2 x 1)

Cancellation of Terms:
We can cancel out the common terms in the numerator and denominator to simplify the expression further:

9P3 = (9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) / (6 x 5 x 4 x 3 x 2 x 1)
= 9 x 8 x 7

Final Result:
Therefore, the value of 9P3 is equal to 9 x 8 x 7, which is 504.

Conclusion:
In this scenario, the value of 9P3 is calculated using the permutation formula. By substituting the given values and simplifying the expression, we find that 9P3 is equal to 504.