{'distinct balls': [0, 0, 0, 1], 'distinct boxes': [0, 0, 0, 1]}
Get the answer to your homework problem.
Try Numerade free for 7 days
We don’t have your requested question, but here is a suggested video that might help.
How many ways are there to distribute six indistinguishable balls into nine distinguishable bins?
$\begingroup$
My approach :-
I first assumed all balls to be similar in nature , so that would give me 5 ways to distribute the balls in the boxes , which will be
2 1 1 1 1
1 2 1 1 1
1 1 2 1 1
1 1 1 2 1
1 1 1 1 2
basically that would be whole number solutions of a+b+c+d+e = 6 where all a,b,c,d,e >=1
Now since all the balls are distinct in nature I multiplied the 5 ways with 6! = giving me a total of 3600 ways , but the answer is given as 1800 ways , where am I going wrong ?
$\endgroup$
Free
100 Questions 200 Marks 120 Mins
Given:
6 distinct balls can be put in 5 distinct boxes.
Calculation:
The number of ways of in n distinct objects can be put into identical boxes, so that neither one of them remains empty.
Since both the boxes and the balls are different , we can choose any box , and every choice is different at any time.
The first ball can be placed in any of the 5 boxes . Similarly , the other balls can be placed in any of the 5 boxes.
The number of ways = 56 = 15625
∴ The number of ways is 15625.
India’s #1 Learning Platform
Start Complete Exam Preparation
Daily Live MasterClasses
Practice Question Bank
Mock Tests & Quizzes
Get Started for Free Download App
Trusted by 3.3 Crore+ Students