(a) Use the multiplicative principle to explain why the number of ways we can select five numbers from {1,2, ...,12} without replacement, where we care about the order of the selection, is equal to 12! 7! (b) Use the multiplicative principle to find the number of ways we can distribute 10 distinguishable ping-pong balls into 4 boxes. Explain your reasoning. You do not need to explicitly evaluate the number. (c) Write down an expression for the number of ways we can distribute 10 distinguish- able ping-pong balls into 4 boxes, where we require that every box contains at least one ball. You do not need to evaluate the expression or explain your answer.
(a) Use the multiplicative principle to explain why the number of ways we can select five numbers from {1,2, ...,12} without replacement, where we care about the order of the selection, is equal to 12! 7! (b) Use the multiplicative principle to find the number of ways we can distribute 10 distinguishable ping-pong balls into 4 boxes. Explain your reasoning. You do not need to explicitly evaluate the number. (c) Write down an expression for the number of ways we can distribute 10 distinguish- able ping-pong balls into 4 boxes, where we require that every box contains at least one ball. You do not need to evaluate the expression or explain your answer.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Transcribed Image Text:(a)
Use the multiplicative principle to explain why the number of ways we can select
five numbers from {1,2,...,12} without replacement, where we care about the order
of the selection, is equal to
12!
7!
(b)
Use the multiplicative principle to find the number of ways we can distribute 10
distinguishable ping-pong balls into 4 boxes. Explain your reasoning. You do not
need to explicitly evaluate the number.
(c)
Write down an expression for the number of ways we can distribute 10 distinguish-
able ping-pong balls into 4 boxes, where we require that every box contains at least
one ball. You do not need to evaluate the expression or explain your answer.
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