Test by Bikram | Mathematics | Test 2 | Question: 12

Question

The total number of functions from the set $\{1,2,3,4, \dots ,10\}$ to the set $\{0,1\}$ that assign $1$ to exactly one of the positive integers less than $10$ are ______.

Answer 1

For integers {1,2,...,9} -

   9 ways for 1 (from set B) to choose an element from set A.

  The remaining 8 numbers will be automatically get mapped to 0 ( of set B) , so only 1 way.

   Total functions  = 9 * 1 = 9.

For integer 10 - 

   As no restriction mentioned , can be mapped to 0 or 1 ( 2 choices )

Total functions = 2 (for int 10) * 9 (ints 1 to 9) = 18

Answer 2

to cases : 10->0 : here 9 ways and 10->1 : here another 9 ways.

Comments

Can u tell me what those functions are?

(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10)

isnot it?

But then total will be 19 :(

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@srestha This is given in the question "that assign 1 to exactly one of the positive integers less than 10 ".
This is really tricky. because they didn't talk about the 10. We are allowed to assign 1 to exactly one of them 1, 2, 3, ... 9.
But as nothing is talk about 10. We can also assign 1 to 10. But when we assign 1 to less than 10 then we assign exactly one of them.

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@ Hemant

ok,got it