Question

We are given n distinct balls and m distinct boxes. m and n are
non-negative integers. Every ball must be placed into a box, but
not every box must have a ball in it. Each box can hold any number
of balls. Let's also assume that **the order in which we put
the balls into the boxes does matter.** (Ex: assume we have
2 balls, a and b, and 3 boxes, 1 2 and 3. two distinct
distributions would be box 1 having a and b, and box 1 having b and
a). How many ways are there to distribute the n balls into the m
boxes?

Answer #1

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STAT Question :
We have 3 distinct balls (indexed Ball 1, Ball 2, Ball 3) and 3
distinct boxes (indexed Box 1, Box 2, and Box 3). Now randomly
assign each ball (independently of other balls) into one of the
boxes.
Fully simplify your final answer to each question into a
fraction or decimal.
Calculate the probability that no box is
empty.
Calculate the probability that ONLY Box 1 is
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NEED HELP !! THANKS

STAT Question
1.We have 3 distinct balls (indexed Ball 1, Ball 2, Ball 3) and
3 distinct boxes (indexed Box 1, Box 2 and Box 3). Now randomly
assign each ball (independently of other balls) into one of the
boxes.
Fully simplify your final answer to each question into a
fraction or decimal.
Calculate the probability that no box is
empty.
Calculate the probability that no box is
empty.
Need Help ! !

We randomly place 200 balls independently in 100 boxes in the
most natural uniform way. That is, each ball is placed
independently from the rest of the balls in such a way that the
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(2010)2010
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10102010
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Fact Suppose there are n distinct objects. There are (n above k)
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