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TS EAMCET · Maths · Permutation Combination

Consider the following statement : (i) Number of one-one functions from set \(A\) to set \(B\), where \(O(A) =m\) and \(O(B) =n(m \leq n)\) is given by \({ }^n P_m\). (ii) Number of ways is which ' \(n\) ' people can be arranged at a circular table is \(\frac{(n-1) !}{2}\) (iii) Number of ways of selecting atleast one thing out of the given \(n\) distinct things is \(2^n-1\). (iv) Number of ways in which \(n\) distinguishable objects can be distributed into \(k\) distinguishable bins is \({ }^n C_{k-1}\). Then which one of the following is true?

  1. A All the statements are true
  2. B All except (iii) are true
  3. C Only (i) and (iii) are true
  4. D Only (ii) is false
Verified Solution

Answer & Solution

Correct Answer

(C) Only (i) and (iii) are true

Step-by-step Solution

Detailed explanation

(i) By definition statement is true (ii) False correct is \((n-1)\) ! (iii) It is also true (iv) It is also false