Question

P(10,10) is equal to:

		1, because their number of elements in the subset is the same as the number of elements in the original set
		10, because we are choosing all 10 elements
		100, because there are 10 ways to choose the first element and 10 ways to choose the second element
		10!, because there are 10 ways to choose the first element, 9 to choose the second, 8 to choose the third, etc.

Answer 1

P(10,10) is equal to:

Answer:

10!, because there are 10 ways to choose the first element, 9 to choose the second, 8 to choose the third, etc

Explanation:
Approach 1

Since we have to choose 10 elements:
We can choose any one of the 10 elements for the first element (in 10 ways),
From the remaining 9, We can choose any one of the 9 elements for the second element (in 9 ways),
From the remaining 8, We can choose any one of the 8 elements for the third element (in 8 ways),

.... (so on)

From the remaining 2, We can choose any one of the 2 elements for the ninth element (in 2 ways),
From the remaining 1, We can choose the tenth element (in 1 way),

Total number of permutation of 10 elements among 10 overall elements = P(10, 10) = 10 * 9 * 8 * ...* 2 * 1 = 10!

Approach 2

The formula for P(n, r) is

n = 10, r = 10

Hence the answer is 10!

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