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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?
Options:
(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?
Solution:
1596 Upvotes
Verified Answer
The correct answer is:
Only (i) and (iii) are true
(i) By definition statement is true
(ii) False correct is $(n-1)$ !
(iii) It is also true
(iv) It is also false
(ii) False correct is $(n-1)$ !
(iii) It is also true
(iv) It is also false
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