We have 9 balls of distinct colours. Calculate the number of ways to arrange them so that following four balls of colour: pink, orange, purple and white are not all together?
Answers
Answer:
Answer will be 345600
Step-by-step explanation:
Solved by Direct Method
Given,
9 balls of distinct colors
To find,
The number of ways to arrange the nine balls so that four balls - pink, purple, orange, and white are not all together.
Solution,
There are 345600 different ways to arrange the nine balls so that four balls - pink, purple, orange, and white - are not all together.
The following approach is a simple way to solve the mathematical issue.
We know that there are nine balls, each of which has a distinct color.
Total number of ways to arrange 9 distinct colored balls in a row = 9! (Equation A)
Now we'll count the no. of various ways that 9 different color balls may be stacked in a row so that pink, purple, orange, and white balls are always together.
We have nine balls in total. Because pink, purple, orange, and white balls are usually together, combine these four balls and treat them as a single ball. As a result, the total number of balls is 6.
These six balls may be stacked in 6! different ways.
We had four balls grouped around us. These four balls may be stacked in 4! different ways.
As a consequence, there are 6! 4! methods to arrange 9 unique color balls in a row so that black, white, red, and green balls are always together. (Equation B)
Based on equations A and B,
The following are the total number of ways to arrange 9 separate color balls in a row so that pink, purple, orange, and white balls are never together;
= 9! − 6!×4!
= 6! ( 9 x 8 x 7 - 4! )
= 6! ( 504 - 24)
= 6! (480)
= 720 x 480
= 345600
Thus, there are 345600 different ways to arrange the nine balls so that four balls - pink, purple, orange, and white - are not all together.