Examples on the Generalized Permutations and Combinations

Published On :2021-02-10 00:13:00

 Ex 1 : How many strings of length 4 be formed from the English alphabet with repetition allowed ? 

Ex 2 : How many ways are there to select 4  pieces with replacement of a fruit from a bowl containing apples , oranges , pears if the order in which the pieces are selected does not matter (there are at least four pieces of each type of fruit) ?

Ex 3 : How many ways are there to select five bills from a cash box containing $1 , $2 , $5 , $10 , $20 , $50 and $100 bills ?

Ex 4 : Suppose that a cookie shop has four different kinds od cookies 

(1) How man different was can 6 cookies be chosen ?

(2) How man different was can 12 cookies be chosen such that at least one cookie is chosen from each type ?

Sol 1 : 

[{26^4} = 456976]

[left( {begin{array}{*{20}{c}} {3 - 1 + 4}\ 4 end{array}} right) = 15] Sol 3 : 

[left( {begin{array}{*{20}{c}} {7 - 1 + 5}\ {7 - 1} end{array}} right) = left( {begin{array}{*{20}{c}} {11}\ 6 end{array}} right) = 462] Sol 4 : (1)

[left( {begin{array}{*{20}{c}} {4 - 1 + 6}\ {4 - 1} end{array}} right) = left( {begin{array}{*{20}{c}} {4 - 1 + 6}\ 6 end{array}} right) = left( {begin{array}{*{20}{c}} 9\ 6 end{array}} right) = 84] (2)

[left( {begin{array}{*{20}{c}} {4 - 1 + 8}\ {4 - 1} end{array}} right) = left( {begin{array}{*{20}{c}} {11}\ 3 end{array}} right) = 165]