Factorials - Find 'n' if (16 - n)! / (14 - n)! = 12

Question:

Find 'n' if (16 - n)! / (14 - n)! = 12

Solution:

(16 - n)! / (14 - n)! = 12

∴ [(16 - n) x (15 - n) x (14 - n)!] / (14 - n)! = 12

∴ [(16 - n) x (15 - n) x ̶(̶1̶4̶ ̶-̶ ̶n̶)̶!̶ ] / ̶(̶1̶4̶ ̶-̶ ̶n̶)̶!̶ = 12

∴ [(16 - n) x (15 - n)] = 12

∴ [(16 - n) x (15 - n)] = 4 x 3

∴ By Comparison

16 - n = 4

∴ n = 16 - 4

∴ n = 12

Answer:

'n' = 12 if (16 - n)! / (14 - n)! = 12

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