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.

How many words,with or without meaning,can be formed using the letters of the word $MONDAY$,assuming that no letter is repeated,if $4$ letters are used at a time?

The number of different permutations of letters that can be formed by taking $4$ letters at a time from the letters of the word '$REPETITION$' is

If $4 \times ^{15}P_r = 3 \times ^{16}P_{r-1}$,then $r = \dots$

There are $9$ chairs in a room on which $6$ persons are to be seated. Out of these,one person is a guest who must occupy one specific chair. In how many ways can they sit?