Hey everyone! Doing permutations at the moment and I found some questions very difficult. There are answers to each question (which are in spoilers), so I really just need the solution. Anyone who can answer any of my questions: thanks so much! :)
Simiplify: Apparently it has got something to do with the identity:
How many ways can 3 potatos be put in 5 boxes if every box can get more than 1 potato?
There are 4 differently coloured shirts. How many arrangements are possible, if you use at least 2 shirts arranged in a row?
You have 6 different colours to paint a cube with. If you are looking at on face androtate the cube and get the same colour, it is considered the same colour. How many ways can you paint this cube, so all of its faces have different colours?
How many ways can 3 onions and 2 zucchini be arranged in a row if they alternate?
The numbers 0 to 5 inclusive must be arranged without repeat. How many ways is this possible, if:
a) it is a 4 digit number, able to be divisible by 5?
b) it is a number < 6000?
c) it is a 3-digit number that is even?
Spoiler
108, 431, 52 respectively
How many palindromic numbers can you make with 5 and 6 digits?
Spoiler
900, 900 respectively
Thanks all! :)