These are the simplest possible counting problems concerning queues.
What have you done on any of them? Where is the difficulty?
Tell us what you do not understand.
Question 1:
Find the number of ways in which five balls of different color can arrange in a row.
Question 2:
A teacher has to select 5 boys from section A, 4 boys from section B and 3 boys from section C for a competition, where section A has total 8 boys, section B has total 7 boys and section C has total 6 boys. How many choices does the teacher have?
Question 3:
A variable name in a programming language must start with an alphabet or characters “_”, next letters can be an alphabet or number. Maximum size for the variable name is 5 characters. How many different variable names are possible?
Question 4:
In how many ways can nine students be partitioned into three teams containing four, three, and two students respectively?
+the First case: the first letter is alphabet .
-The first letter has 26 choices
-The 2sd letter has 36-1 choices (26 alphabetic characters and 10 numbers)
-The 3rd letter has 36-2 choices.
-...
-...
So , we have :26 + 26*35 + 26*35*34 + 26*35*34*33 + 26*35*34*33*32 =: S1 choices for this case.
+the Second case: the first letter is "_" character.
-The first has 1 choice.
-The 2sd letter has 36 choices.
-The 3rd letter has 36-1 choices.
-...
So , we have :36 + 36*35 + 36*35*34 + 36*35*34*33 =: S2
(considering that "_" is not a variable name)
The final result is S1+S2 .
Not when you divide the problem into sub-cases.
For example, say the problem goes something like this "...find how many combinations for at least 3 students..."
You can simplify the problem by finding:
exactly 1 student
exactly 2 students
exactly 3 students
And then add up the combinations in all the sub-cases.
Question 2:
A teacher has to select 5 boys from section A, 4 boys from section B and 3 boys from section C for a competition, where section A has total 8 boys, section B has total 7 boys and section C has total 6 boys. How many choices does the teacher have?
Yes you are correct we must multiply and not add to answer this partiucular question.
Hi Soronban.
Another way :
We choose 4 students from 9 students :
After that choosing 3 students from 5 students :
And the final , choosing 2 from 2 :
So , the result is : * * = 1260.
@ Soronban : Would you like to tell how we receive the function that you gave ? I mean that what way you think about the question 4?