the total number of ways in which 5 balls of different colours can be distributed among 3 persons so that each person get at least one ball is?
Koi acche way Mein explain karo yaar plz......
To find the total number of ways in which 5 balls of different colors can be distributed among 3 persons such that each person gets at least one ball, we can use the concept of permutations and combinations.
Let's break down the problem step by step:
Step 1: Distribute 1 ball to each person
Since each person must receive at least one ball, we start by distributing one ball to each person. After this step, we will be left with 2 balls to distribute.
Step 2: Distribute the remaining 2 balls among the 3 persons
Now, we have 2 balls left and 3 persons to distribute them among. To find the number of ways to do this, we can use combinations.
We need to distribute 2 balls among 3 persons, which means we need to find the number of different combinations of 2 out of 3.
The formula for combinations is given by:
C(n, r) = n! / (r! * (n - r)!)
Where n is the total number of items, and r is the number of items chosen at a time. In our case, n = 3 and r = 2.
C(3, 2) = 3! / (2! * (3 - 2)!)
= 3! / (2! * 1!)
= (3 * 2 * 1) / (2 * 1 * 1)
= 3
So, there are 3 different ways to distribute the remaining 2 balls among the 3 persons.
Step 3: Multiply the results from Step 1 and Step 2
To get the total number of ways, we need to multiply the total number of ways from Step 1 and Step 2.
Total number of ways = 1 * 3 = 3
Therefore, there are 3 different ways in which 5 balls of different colors can be distributed among 3 persons so that each person gets at least one ball.