If the letters of the word $SACHIN$ are arranged in all possible ways and these words are written out as in a dictionary,then the word $SACHIN$ appears at serial number:

The number of words,with or without meaning,that can be formed by taking $4$ letters at a time from the letters of the word $'SYLLABUS'$ such that two letters are distinct and two letters are alike,is

Eight chairs are numbered $1$ to $8$. Two women and three men wish to occupy one chair each. First,the women choose chairs from amongst the chairs marked $1$ to $4$,and then the men select the chairs from amongst the remaining. The number of possible arrangements is

Consider all possible permutations of the letters of the word $EARTHQUAKE$. The number of permutations containing the word $RAHU$ is:

If ${ }^{22} P_{r+1}:{ }^{20} P_{r+2}=11: 52$,then $r=$

Eight different letters of an alphabet are given. Words of four letters from these are formed. The number of such words with at least one letter repeated is: