Factorial Notation
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Question 1 of 4
1. Question
On the following events, write $$\mathsf{P}$$ if it is a Permutation or $$\mathsf{C}$$ if it is a Combination.
`(i)` Forming a doubles team for tennis: (C, c)`(ii)` Creating a password for a website: (P, p)`(iii)` Selecting the `1`st, `2`nd and `3`rd rankings in a car race: (P, p)`(iv)` Being a member of a jury: (C, c)
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Permutation
An arrangement where order is important.Combination
A grouping where order is not important.In each item, check whether the order is important or not`(i)` Forming a doubles team for tennis:The order of tennis players in forming a doubles team for tennis is not important.Hence, this is a Combination`(ii)` Creating a password for a website:The order of characters in creating a password for a website is important.Hence, this is a Permutation`(iii)` Selecting the `1`st, `2`nd and `3`rd rankings in a car race:The order or rankings in a car race is important.Hence, this is a Permutation`(iv)` Being a member of a jury:The order of being selected as a member in a jury is not important.Hence, this is a Combination`(i)` $$\mathsf{C}$$`(ii)` $$\mathsf{P}$$`(iii)` $$\mathsf{P}$$`(iv)` $$\mathsf{C}$$ 

Question 2 of 4
2. Question
Evaluate`5!` (120)
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Factorial Formula
`n! = n*(n1)*(n2)*…*3*2*1`Substitute the given `n=5` to the formula`n!` `=` `n*(n1)*(n2)*…*3*2*1` Factorial Formula `5!` `=` `5*4*3*2*1` Substitute known values `=` `120` `120` 
Question 3 of 4
3. Question
Evaluate`(12!)/(10!)` (132)
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Factorial Formula
`n! = n*(n1)*(n2)*…*3*2*1`Apply the formula to the fraction`n_1` `=` `12` `n_2` `=` `10` `(n_1!)/(n_2!)` `=` `(n_1*(n_11)*(n_12)*…*3*2*1)/(n_2*(n_21)*(n_22)*…*3*2*1)` Factorial Formula `(12!)/(10!)` `=` $$\frac{12\cdot11\cdot\color{#CC0000}{10\cdot9\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1}}{\color{#CC0000}{10\cdot9\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1}}$$ Substitute known values `=` `12*11` Cancel like terms `=` `132` `132` 
Question 4 of 4
4. Question
Evaluate`(9!)/(0!)` (362880)
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Factorial Formula
`n! = n*(n1)*(n2)*…*3*2*1`Zero Factorial
`0! = 1`Apply the formula to the fraction`n_1` `=` `9` `n_2` `=` `0` `(n_1!)/(n_2!)` `=` `(n_1*(n_11)*(n_12)*…*3*2*1)/(n_2*(n_21)*(n_22)*…*3*2*1)` Factorial Formula `(9!)/(0!)` `=` $$\frac{9\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1}{1}$$ `0! =1` `=` `362 880` `362 880`
Quizzes
 Factorial Notation
 Fundamental Counting Principle 1
 Fundamental Counting Principle 2
 Fundamental Counting Principle 3
 Combinations 1
 Combinations 2
 Combinations with Restrictions 1
 Combinations with Restrictions 2
 Combinations with Probability
 Basic Permutations 1
 Basic Permutations 2
 Basic Permutations 3
 Permutation Problems 1
 Permutation Problems 2
 Permutations with Repetitions 1
 Permutations with Repetitions 2
 Permutations with Restrictions 1
 Permutations with Restrictions 2
 Permutations with Restrictions 3
 Permutations with Restrictions 4