[Math] How many arrangements are there of the letters in word with restriction

combinatoricsprobabilitystatistics

How many arrangements are there of the letters in REPETITIVENESS such that
the Ss are consecutive AND the first I comes (somewhere) before the first E ?

What i though is by viewing ss as one letter , it would solve the first restriction .

And i have no idea how to count the second restriction .

there are 13 spaces considering that ss is one space

there are 2 i and 4 e

still cant figure this out 🙁

Best Answer

First treat I and E as the same letter. Then, once you have decided where in the final arrangement they go, how many ways are there to distribute Is and Es to those positions, keeping in mind that the first of them must be an I?