If there are six periods in each working day of a school, in how many ways can one arrange 5 subjects such that each subject is allowed at least one period?

  Find the number of permutations of the letters of the word ALLAHABAD.

  In how many way can the letters of the word ‘PENCIL’ be arranged so that N is always next to E?

  Find the number of different 8-letter words formed from the letters of the word TRIANGLE if each word is to have consonants never together.

  In how many ways can 5 books on Chemistry and 4 books on Physics be arranged on a shelf so that the books on same subject remain together?

  In how many ways can 5 children be arranged in a line such that(i) two of them, Ram and Shyam, are always together, (ii) two of them, Ram and Shyam, are never together.

  There are 8 students appearing in an examination, of which 3 have to appear in a mathematics paper and the remaining 5 in different subjects. In how many ways can they be made to sit in a row if the candidates in mathematics cannot sit next to each other?

  In how many ways can 4 boys and 3 girls be seated in a row so that no two girls are together?

  The principal wants to arrange 5 students on the platform such that the boy SALIM occupies the second position and such that the girls SITA is adjacent to the girl RITA. How many such arrangements are possible?

  Three married couples are to be seated in a row having six seats in a cinema hall. If spouses are to be seated next to each other, in how many ways can they be seated? Find also the number of ways of their seating if all the ladies sit together?