How many permutations are there for the letters in the word #" machines"?#

↳Redirected from "Suppose that I don't have a formula for #g(x)# but I know that #g(1) = 3# and #g'(x) = sqrt(x^2+15)# for all x. How do I use a linear approximation to estimate #g(0.9)# and #g(1.1)#?"
1 Answer
Greypo · EZ as pi
Aug 19, 2017

#40,320#

Explanation:

There are #8# unique letters.

There are eight options for the first position.

When one is taken, there are seven options for the second position, and so on..

Therefore, the answer is:

# 8! = 8 xx 7 xx 6 xx 5 xx 4 xx 3 xx 2 xx 1#

Permutations include different orders of the same letters.

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