How many anagrams can be created from the word 'masslessness' if the new words do not need to be meaningful?

332640 anagrams

Step-by-step explanation:

Given the word:

'masslessness'

Total number of letters= 12

Number of S = 6

E =2

The rest are one each.

The number of possible arrangements can be written as;

N = 12!/(6!2!)

N = 332640

We can solve this problem using discriminant.

x^2-4x-12's discriminant is

(-4)^2-4*-12=16+48 which is clearly larger than 0

This means that it crosses over the axes 2 times.

In case you don't know what discriminant is, its in equation ax^2+bx+c

the discriminant is b^2-4ac.

If its positive it has 2 crosses with x axis, if negative then 0 crosses, if 0 then 1 cross.

Hope this helped at least a little bit :D