2. Examples
1. Find `5 !`
`5! = 1 * 2 * 3 * 4 * 5=120`
2. Find `(3 !)/(2 !)`
`(3 !)/(2 !)`
`=(3*2 !)/(2 !)`
`=3`
3. Find `{::}^3P_2`
`{::}^n P_r = (n!) / ((n-r)!)`
`{::}^3P_2`
`=(3!) / ((3 - 2)!)`
`=(3!) / (1!)`
`=(3 * 2 * (1)!) / (1!)`
`=3 * 2`
`=6`
4. Find `{::}^3C_2`
`{::}^n C_r = (n!) / ((r!) (n-r)!)`
`{::}^3C_2`
`=(3!) / ((2!)(3 - 2)!)`
`=(3)/(1)`
`=3`
5. How many words can be formed by using all letters of the word DAUGHTER.
The word DAUGHTER contains 8 letters.
When the vowels AUE are always together, they can be supposed to form one letter.
Then, we have to arrange the letters DGHTR (AUE).
Number of ways of arranging these letters `= 6! = 720` ways
The word AUE contains 3 letters.
Number of ways of arranging these letters `= 3! = 6` ways
Required number of ways `= 720 * 6 = 4320`
6. From a group of 6 Men, 5 Women. In how many ways a committee of 3 Men, 2 Women can be formed ?
(3 Men out of 6), (2 Women out of 5) are to be chosen
Required number of ways `= {::}^6C_3*{::}^5C_2`
`=(6!) / ((3!)(6 - 3)!)*(5!) / ((2!)(5 - 2)!)`
`=(6 * 5 * 4)/(3 * 2 * 1)*(5 * 4)/(2 * 1)`
`=20*10`
`=200`
7. Find list for `n=5,r=3`, Is order important=true, Is repetition allowed=true, List variables=A
`n=5,r=3,"List variables"=A,B,C,D,E`
Permutation with repetition :
Formula ` = n^r = 5^3 = 125`
List are (total = 125) :
{A,A,A}, {A,A,B}, {A,A,C}, {A,A,D}, {A,A,E}, {A,B,A}, {A,B,B}, {A,B,C}, {A,B,D}, {A,B,E}, {A,C,A}, {A,C,B}, {A,C,C}, {A,C,D}, {A,C,E}, {A,D,A}, {A,D,B}, {A,D,C}, {A,D,D}, {A,D,E}, {A,E,A}, {A,E,B}, {A,E,C}, {A,E,D}, {A,E,E}, {B,A,A}, {B,A,B}, {B,A,C}, {B,A,D}, {B,A,E}, {B,B,A}, {B,B,B}, {B,B,C}, {B,B,D}, {B,B,E}, {B,C,A}, {B,C,B}, {B,C,C}, {B,C,D}, {B,C,E}, {B,D,A}, {B,D,B}, {B,D,C}, {B,D,D}, {B,D,E}, {B,E,A}, {B,E,B}, {B,E,C}, {B,E,D}, {B,E,E}, {C,A,A}, {C,A,B}, {C,A,C}, {C,A,D}, {C,A,E}, {C,B,A}, {C,B,B}, {C,B,C}, {C,B,D}, {C,B,E}, {C,C,A}, {C,C,B}, {C,C,C}, {C,C,D}, {C,C,E}, {C,D,A}, {C,D,B}, {C,D,C}, {C,D,D}, {C,D,E}, {C,E,A}, {C,E,B}, {C,E,C}, {C,E,D}, {C,E,E}, {D,A,A}, {D,A,B}, {D,A,C}, {D,A,D}, {D,A,E}, {D,B,A}, {D,B,B}, {D,B,C}, {D,B,D}, {D,B,E}, {D,C,A}, {D,C,B}, {D,C,C}, {D,C,D}, {D,C,E}, {D,D,A}, {D,D,B}, {D,D,C}, {D,D,D}, {D,D,E}, {D,E,A}, {D,E,B}, {D,E,C}, {D,E,D}, {D,E,E}, {E,A,A}, {E,A,B}, {E,A,C}, {E,A,D}, {E,A,E}, {E,B,A}, {E,B,B}, {E,B,C}, {E,B,D}, {E,B,E}, {E,C,A}, {E,C,B}, {E,C,C}, {E,C,D}, {E,C,E}, {E,D,A}, {E,D,B}, {E,D,C}, {E,D,D}, {E,D,E}, {E,E,A}, {E,E,B}, {E,E,C}, {E,E,D}, {E,E,E}
This material is intended as a summary. Use your textbook for detail explanation.
Any bug, improvement, feedback then
|
