On a trip You want to send postcards to 12 friends. In the shop, there are only
ID: 3123296 • Letter: O
Question
On a trip You want to send postcards to 12 friends. In the shop, there are only 3 kinds of postcards. In how many ways can you send the postcards if: (a) there is a large number of each kind of postcards, and you want to send one card for each friend. (b) there is a large number of each kind of postcards, you are willing to and send one or more postcards to each friend, but no one should get two identical postcards. (c) the shot has only 4 of each kind of postcard, and you want to send one card to each friend.Explanation / Answer
(a) Since there are 12 friends and each one will be sent one postcard, a total of 12 postcards will be sent.
The first postcard can be of 3 kinds.
The second postccard can be of 3 kinds.
The third postcard can also be of 3 kinds and so on.
So the total number of ways of sending the postcards = 3*3*3...... 12 times
= 312
(b) Each friend can get one, two or three kinds of postcards.
So the number of ways of sending one post card to a friend = 3C1 = 3
Number of ways of sending two post cards to a friend = 3C2 = 3
Number of ways of sending three post cards to a friend = 3C3 = 1
So number of ways of sending postcard to a single friend = 3+3+1 = 7
Since there are 12 friends and by earlier result 312 different postcards can be sent to all friends, total number of ways to send postcards = 7*312
(c) Since the shot has 4 of each kind of postcard and there are 3 kinds, there are a total of 12 postcards. As there are 12 friends, each will receive 1 postcard each.
So the task is to distribute 12 objects to 12 people with 3 kinds of 4 each.
This can be done in 12! / (4!)3 ways.