Question

Let A be the set (1, 2, 3, 4, 5, 6)
No. of functions from A to A, such that range off
has exactly 5 elements is k, then sum of digit of
number kis​

Answer 1

SOLUTION :

GIVEN

Let A be the set { 1, 2, 3, 4, 5, 6 }

No. of functions from A to A , such that

range of f has exactly 5 elements is k

TO DETERMINE

The sum of digit of number k

CONCEPT TO BE IMPLEMENTED

If a set A contains n elements and B be a set containing m elements then the number of functions from A to B

$= \sf{} {m}^{n}$

EVALUATION

Here A = { 1, 2, 3, 4, 5, 6 }

So n ( A ) = 6

Let B be the range set of a function f

Then by the given condition n ( B ) = 5

So the total number of functions

$\sf{} = {5}^{6} = 15625$

So by the given information

$\sf{}k = 15625$

Hence the sum of digit of number k

$= \sf{}1 + 5 + 6 + 2 + 5$

$= \sf{}19$

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LEARN MORE FROM BRAINLY

If n(A) = 300, n(A∪B) = 500,

n(A∩B) = 50 and n(B′) = 350,

find n(B) and n(U)

https://brainly.in/question/4193770