In how many ways 8 examination papers be arranged in a line so that the best and worst papers never come together?
Six papers are set in an examination of which two are mathematical. In how many different orders can the papers be arranged so that (i) the two mathematical papers are together and (ii) the two mathematical papers are not consecutive?
How many numbers between 1000 and 10,000 can be formed with the digits 1, 2, 3, 4, 5, 6, 7, 8, 9? How many of them are odd?
The figures 1, 2, 3, 4, 5 are written in every possible order. How many of the numbers so formed will be greater than 23000?
Find the number of ways in which n books can be arranged on a shelf so that two particular books are not together.
In how many ways can 3 books on Commercial Mathematics and 5 books on Secretarial Practice be placed on a shelf so that books on the same subject always remain together? (no two books are identical).
In how many ways can be letters of the word VIOLENT be arranged so that the vowels I, O, E, occupy even places only.
(a) In how many ways can 8 different beads be strung on a necklace? (b) In how many ways can 8 boys from a ring
A library has 5 copies of one book, 4 copies of each of two books, 6 copies of each of three books, and single copies of 8 books. In how many ways can all the books be arranged?
Find the number of permutations of the letters of the word “SIGNAL’ such that the vowels may occupy only odd positions.