How many ways can n books be placed on k distinguishable shelves?
a. If no two books are the same ,and the positions of the books on the shelves does not matter?
b. If no two books are the same,and the positions of the books on the shelves matter?
If there are N books and K shelves then for
a) The answer will be (N+(K-1))C(N) because the problem can be reduced to choosing N books from N+(K-1)) elements where K-1 is the Shelf divider count. Here only the number of ways the books can be placed is evaluated.
b) Here the above number is multiplied by N! as there are N! ways the books can be rearranged in each choice made above. Therefore the answer is (N+(K-1))C(N)*(N!).
A correspondent writes 7 letters and addresses 7 envelopes, one for each letter. In how many ways can all of the letters be placed in the wrong envelopes?
There are 12 different chocolates placed on a table along a straight line. In how many ways can a person choose 4 of them such that no 2 of the chosen chocolates lie next to each other?
In how many ways the letters of the word ‘CHEKOSLOVAKIA’ can be arranged such that “SL” always comes together and ‘H’ and ‘I’ at the end places?