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In nPr = n (n–1) (n–2) ………………(n–r–1), the number of factor is
  • a)
    n
  • b)
    r–1
  • c)
    n–r
  • d)
    r
Correct answer is option 'D'. Can you explain this answer?
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In nPr = n (n–1) (n–2) ……………...
Permutation Formula

The permutation formula is used to find the number of ways to arrange a set of objects in a specific order. It is denoted by nPr, where n represents the total number of objects and r represents the number of objects taken at a time. The formula for permutations is:

nPr = n! / (n-r)!

where "!" represents the factorial function.

Explanation

Given, nPr = n (n1) (n2) (nr1)

Here, n represents the total number of objects taken at a time and r represents the number of objects taken at a time.

The formula for permutations is:

nPr = n! / (n-r)!

We can rewrite the given formula as:

nPr = n * n1 * n2 * ... * nr1

Comparing the two formulas, we can see that:

- n represents the total number of objects taken at a time, which is the same as n in the permutation formula
- r represents the number of objects taken at a time, which is the same as the number of factors in the given formula

Therefore, the correct answer is option 'D', which states that the number of factors is r.
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In nPr = n (n–1) (n–2) ………………(n–r–1), the number of factor isa)nb)r–1c)n–rd)rCorrect answer is option 'D'. Can you explain this answer?
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