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Unit 12: Permutation
Notes
Notes Make note of the manner we managed that cancellation. We expanded the factorial
expressions enough that we could observe where I could cancel off duplicate factors.
Although we had no idea what n might be, I could still cancel.
Example: The senior choir has rehearsed five songs for an upcoming assembly. In how
many different orders can the choir perform the songs?
Solution:
There are five ways to choose the first song, four ways to choose the second, three ways to
choose the third, two ways to choose the fourth, and only one way to choose the final song.
Using the fundamental counting principle, the total number of different ways is
5 × 4 × 3 × 2 × 1 = 5!=120
The choir can sing the five songs in 120 different orders.
Example:
9!
3!6!
7
8
9 6!
3!6!
= 84
Example:
6! is a factor of 10!. For,
10! 1 2 3 4 5 6 7 8 9 10
6! 7 8 9 10
Example:
8! 1 2 3 4 5 6 7 8
6 7 8 6 56 336
5! 1 2 3 4 5
Self Assessment
Fill in the blanks:
3. Factorials are just products, symbolized by an ................................. .
4. Factorial indicates the number of different ................................. in which one can arrange or
place set of items.
5. A factorial symolizes the multiplication of ................................. natural numbers.
6. n! means the ................................. of all the whole numbers from 1 to n; that is, n! = 1 × 2 × 3
× ... × n.
7. 0! is defined to be equal to ................................. , not 0.
LOVELY PROFESSIONAL UNIVERSITY 161
