Question

how many different distinguishable orders can the letters of the word precalculus be arranged

Answer 1

This is a problem of permutation or arrangements, the word PRECALCULUS has 11 letters, of which 3 letters appear twice, we want to get the number of indistinguishable arrangements, this is how we do it,

$P_r^n=\frac{n!}{(n-r)!}$

For our problem, what we do is

$=\text{ }\frac{11!}{2!\text{ 2! 2!}}\text{ = }\frac{11!}{8}\text{ = 4989600 orders}$