In how many ways can the letters of the word $TRIANGLE$ be rearranged?

$A$ number lock consists of three rings. If the $1^{st}$ ring is marked with digits $0$ to $9$,the $2^{nd}$ ring is marked with prime numbers greater than $2$ but less than $30$,and the $3^{rd}$ ring is marked with all vowels,find the total number of unsuccessful attempts.

All possible numbers are formed using the digits $1, 1, 2, 2, 2, 2, 3, 4, 4$ taken all at a time. The number of such numbers in which the odd digits occupy even places is

How many distinct $9$-digit numbers can be formed by rearranging the digits of the number $223355888$ such that all odd digits occupy even positions?

Find the number of arrangements of the letters of the word $INDEPENDENCE$. In how many of these arrangements do the words begin with $I$ and end in $P$?

We are to form different words with the letters of the word $INTEGER$. Let $m_1$ be the number of words in which $I$ and $N$ are never together and $m_2$ be the number of words which begin with $I$ and end with $R$,then $m_1/m_2$ is equal to