Question

five balls are placed at random in five buckets.What is the probability that bucket has a ball

Answer 1

Each ball can be placed in any one of the bucket. Therefore, the number of ways in which a ball can be placed in a bucket is 5.

The number of ways in which five balls can be placed in 5 buckets are $5^5=3125.$

If each bucket has a ball: $5!=120.$

The probability that each bucket has a ball

$${5! \over 5^5}={120 \over 3125}={24 \over 625}=0.0384$$