In how many different ways can the letters of the word '$PRAISE$' be arranged?

In a city,no two persons have an identical set of teeth,and there is no person without a tooth. Also,no person has more than $32$ teeth. If we disregard the shape and size of the teeth and consider only the presence or absence of a tooth at each of the $32$ positions,then the maximum population of the city is:

$20$ persons are invited for a party. In how many different ways can they and the host be seated at a circular table,if two particular persons are to be seated on either side of the host?

In a club election,the number of contestants is one more than the number of maximum candidates for which a voter can vote. If the total number of ways in which a voter can vote is $62$,then the number of candidates is:

$6$ boys and $5$ girls sit in a line such that $(I)$ no two girls sit together $(II)$ all the girls sit together. If $p$ is the number of arrangements in case $(I)$ and $q$ is the number of arrangements in case $(II)$,then $p/q =$

$A$ dictionary is printed consisting of $7$-letter words only that can be formed using the letters of the word $CRICKET$. If the words are arranged in alphabetical order,as in an ordinary dictionary,then the number of words before the word $CRICKET$ is: