If 3 sisters and 8 other girls are together playing a game, then the number of ways in which all the girls are seated around a circle such that the three sisters are not seated together, is

If $x$ and $y$ represent the number of arrangements of the letters of word ATRAPATRAM such that (i) all A's are together and (ii) no two A's are together respectively, then $x+y$

Numbers between 1 and 10,000 are formed using the digits 2 and 3 only once and the digit 4 twice. If the numbers thus formed are arranged in increasing order and $x, y$ represent the ranks of 4324 and 324 respectively then $x-y=$

The total number of three digit and five digit integers which can be formed by using the digits $0,1,2,3,4,5$ but using each digit not more than once in each number is