Permutations And Combinations

To solve for ⁸¹P₂ - ⁸¹C₂, we need to understand the formulas for permutations and combinations.

The permutation formula ⁿP_r is:

For n = 81 and r = 2:

⁸¹P₂ = 81! / (81-2)! = 81! / 79!

This simplifies to:

81 × 80 = 6480

Next, the combination formula ⁿC_r is:

For n = 81 and r = 2:

⁸¹C₂ = 81! / [2!(81-2)!] = 81! / [2! × 79!]

This simplifies to:

81 × 80 / 2 = 6480 / 2 = 3240

The value of ⁸¹P₂ - ⁸¹C₂ is:

6480 - 3240 = 3240