Question

PROBLEM #5: Using a computer that can perform 109 calculations a second, roughly how long would it take to try all possible permutations of 15 different letters? (Show all calculation steps) PROBLEM #6: Using a computer that can perform 109 calculations a second, roughly how long would it take to try all possible permutations of 15 different letters? (Show all calculation steps)

Answer 1

Step-by-step explanation:

formula to calculate the permutations:

nPr = n! / (n - r)!

where

n = total number of objects

r = number of objects selected

according to the question we have to calculate the permutations of 15 different letters so,

n = 26

r = 15

thus, nPr = 26! / (26 - 15)! = 26! / 11!

roughly, the possible permutations we get will be a number in trillions.

the computer which we are using can perform,

109 calculations in 1 second

6,540 calculations in 1 min

3,92,400 calculations in 1 hour

thus,

in a rough estimation if a computer is solving million instructions in 2 hours time it can solve trillion instructions in 4 hours.