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How many different ways can 4 identical items be put into 6 possible spaces? How about 4 identical items in 7 possible spaces? & lastly, 5 identical items in 8 possible spaces?

How many different ways can 4 identical items be put into 6 possible spaces? How about 4 identical items in 7 possible spaces? & lastly, 5 identical items in 8 possible spaces?

World of Chemistry, 3rd edition
World of Chemistry, 3rd edition
3rd Edition
ISBN:9781133109655
Author:Steven S. Zumdahl, Susan L. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan L. Zumdahl, Donald J. DeCoste
Chapter13: Gases
Section: Chapter Questions
Problem 49A
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How many different ways can 4 identical items be put into 6 possible spaces?
How about 4 identical items in 7 possible spaces?
& lastly, 5 identical items in 8 possible spaces? 

Expert Solution
Step 1

The number of ways to put "n" identical items into "k" possible spaces can be calculated using the combination formula:  C(k,n) = k! / (n! (k-n)!) 

where "!" denotes the factorial symbol. In this formula, "n" represents the number of items to be placed, and "k" represents the number of available spaces.  So, if you have "n" identical items and "k" possible spaces, you can calculate the number of ways to place them by applying the formula above

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