Question

In how many ways can 3 balls be arranged in 9 different boxes in a row such that the number of balls image box does not exceed one

Answer 1

Answer:

Thus, the total no. of ways are 8*7*6*243 = 81648.

Answer 2

Given: 3 balls have to be arranged in 9 different boxes in a row such that number of balls in each box does not exceed one

To find: Total number of ways to do the task

Explanation: Since there are 3 balls and 9 boxes and the maximum number of balls a box can hold is 1, we need to select 3 boxes out of the given 9 boxes.

Ways to select 3 boxes out of 9=

$\binom{9}{3}$

= 9! / 6! 3!

= 9*8*7 / 3*2

= 84

Now, we need to arrange 3 balls in the 3 chosen boxes.

Total number of ways to do this= 3! = 6

Therefore, total number of ways= 84*6= 504

Therefore,3 balls can be arranged in 9 different boxes in 504 ways.