## mathmath333 one year ago Question

1. mathmath333

\large \color{black}{\begin{align} & \normalsize \text{Find the number of ways or rearranging the word}\quad \Large \rm INSTITUTE\hspace{.33em}\\~\\ \end{align}}

2. anonymous

This is a permutation

3. anonymous

9*8*7*6*5*4*3*2*1=

4. anonymous

5. mathmath333

u mean $$\large 9!$$

6. anonymous

yeah I do

7. phi

you have to account for repeated letters

8. anonymous

That's why it's 9 exclamation happy mathy day

9. mathmath333

hmm that is given as wrong

10. rhr12

Opps!! Idk what is that.

11. freckles

$\frac{ \text{ total number of letters }!}{\text{ repetitions of letter i}!}$ where i can be a,b,c,....z

12. freckles

for example if we had the word ball it would be 4!/2!

13. freckles

or if we had the word mississippi it would be $\frac{11!}{4! \cdot 4! \cdot 2!}$

14. freckles

where one of those 4's account for the amount of s the other 4 account for the amount of i and where 2 account for the amount of p

15. mathmath333

(9/2*3)!