How many ways are there to divide a red bracelet, a yellow bracelet, a green bracelet, and a black bracelet among 4 people if each person can receive at most two bracelets? Each bracelet must be given to someone.
Let's take a look Pangolin14
I am assuming that the people are all different.
division of bracelets.
4,0,0,0 4 ways
3,1,0,0 4 ways to chose odd one out, 4 ways to choose who to give the 3 ways to choose who gets the one.
4*4*3 = 48 ways
2,2,0,0 4C2 /2 = 3 ways to pair the bracelets
4 ways to chose the allocate the fist pair, 3 ways to allocate the 2nd pair
3*4*3 = 36 ways
2,1,1,0 4C2 = 6 ways to choose the pair.
4! ways to order the people = 24 ways
6*24 = 144 ways
1,1,1,1 4! ways = 24 ways
4+48+36+144+24 = 256 ways
I am happy to discuss this if you want guest or Pangolin14