Number arranging

Question

The number of ways of arranging the 26 letters of the English alphabet = 26!. If a computer prints these arrangements at the rate of 1000 per second, how long will this take?

Answer 1

Hi Chek,

 

26! = 26×25×24×...×2×1 = 4.0.32914611×10²⁶, using your calculator.

 

  If 1000 arrangements can be processed by a computer per second, then divide the above number by 1000.

 

t = 4.032914611×10²⁶ / 1000 = 4.032914611×10²³ sec

 

This is a huge amount of time.

 

t = (4.032914611×10²³ sec)(1 hour / 3600 sec)(1day / 24 hour)(1 year / 365 days) = 1.2788×10¹⁶ years

 

This is 12,788,288 billion years. The age of the Universe is about 13.7 billion years to give you some perspective.