Suppose that a random number generator randomly generates a number from 1 to 65. Once a specific number is generated, the generator will not select that number again until it is reset. If a person uses the random number generator 65 times in a row without resetting, how many different ways can the numbers be generated?

65!

65! = 8. 2547650592 * 10^ 90 approximately

Step-by-step explanation:

A random number generator randomly generates a number from 1 to 65.

Once a specific number is generated, the generator will not select that number again until it is reset.

The number of ways it can be used is = 65!

65! = 8. 25476505* 10^ 90 approximately

For this case we have the following table:
 Number of eggs Number of omelets
 18   ?
 9     3
 6     2
 3     1
 We observe that the function is linear.
 The equation of the line is:
 y-yo = m (x-xo)
 Where,
 m = (y2-y1) / (x2-x1)
 m = (6-3) / (2-1)
 m = (3) / (1)
 m = 3
 (xo, yo) = (1, 3)
 Substituting:
 y-3 = 3 (x-1)
 Rewriting:
 y = 3x - 3 + 3
 y = 3x
 For 18 eggs we have:
 18 = 3x
 Clearing x:
 x = 18/3
 x = 6
  
 you can make 6 omelets with 18 eggs