If P(10,R) = 90, What Is R?

If p(10,r) = 90, what is r?

 

Answer:

r = 2

Step-by-step explanation:

P (n, r) = n!/(n-r)!

Given:

P(10,r) = 90

Where:

n =  10

r = Unknown

Solve for r:

10!/(10-r)! = 90

Cross-multiply:

10!/90 = (10-r)!

10×9×8×7×6×5×4×3×2×1/90  = (10-r)!

3,628,800/90 = (10-r)!

40,320 = (10 - r)!

8! = 10! - r!

r = 10 - 8

r = 2

Check:

P(10, 2) = 90

10!/(10-2)! = 90

10!/8! = 90

10 × 9 ×8×7×6×5×4×3×2×1/8×7×6×5×4×3×2×1 = 90

10 × 9 = 90

90 = 90  (True)


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