IIT JEE , AIEEE Forum - Mathematics , Algebra

vish0001

let a function be defined as f : { 1 , 2 , 3 , 4 , 5 }

{ 1 , 2 , 3 , 4 , 5 }

then the number of ways in which f ( i )

i is ???

i m getting the answer as 20 ( ⁵C₁X 4 )

but the answer given is 44 .... by using the dearrangement forumula we are getting the answer as 44 ....... but what';s wrong in my logic ? please do reply !

vish0001

arey yaar pls reply

vish0001

helpppppppppppppppppppppppppppppppppppppppppppp

thevyzz

think that all the ten elements are individual

no of combinations = 10C2 = 90/2

since the function is in only one direction

no of possible combos = 45

out of these one is correct

so the ans is 44

faith

by the dearrangement u get only one-one and onto functions which satisfy f(i) /= i .
But here in this ques all fuctions, whether many one or even into are accepted . the only condition is f(i) /= i

in your logic, you hafve not found the no. of possible functions, as there each and every elt. of the domain has to be taken , ( and not any one : 5C1 )

vish0001

but yaar what;s wrong in my method ??

vish0001

faith yaar ... i have applied the condition of f(i) not equal to i
not able to understand this logic pls help yar

vish0001

replyyyyy plssssssssssssssssss

priyesh

Hi vish
yaar the answer will be 44 if the function is bijective i.e one-one & onto. but in this case since there is no condition on the function hence every element in the domain can have 1 out of the four images.
for eg: 1 can have either of 2,3,4,5 as it's images
therefore every element in domain can have the image in range in four ways hence no. of ways = 4 * 4 * 4 * 4 *4 = 1024

vish0001

yaar pls temme what;s wrong in my method pls
a little detail pls this concept is a little troupblesome for me

vish0001

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vish0001

yaar pls temme what;s wrong in my method pls
a little detail pls this concept is a little troupblesome for me

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