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Find the number of ways of distributing n balls in n cells. What will be the number of ways if each cell must be occupied? - Mathematics and Statistics

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Sum

Find the number of ways of distributing n balls in n cells. What will be the number of ways if each cell must be occupied?

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Solution

For filling first cell, n balls are available.
First cell is filled in n ways.
Second cell is filled in (n – 1) ways
Third cell is filled in (n – 2) ways and so on.
nth cell is tilled in one way.
Required number
= n (n – 1) (n – 2) … 1
= n!

Concept: Introduction of Permutations and Combinations
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APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board
Chapter 6 Permutations and Combinations
Miscellaneous Exercise 6 | Q 4. (ii) | Page 92
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