Match the items of List-$I$ to the items of List-$II$:
List-$I$ List-$II$
$(A)$ The number of ways of not selecting $(n-r)$ things from $n$ different things $(I)$ $1+n+{ }^n C_2+\ldots+{ }^n C_r$
$(B)$ $(n-r+1) \cdot{ }^n C_{r-1}$ $(II)$ $(r+1) \cdot{ }^n C_{r+1}$
$(C)$ The number of ways of selecting at least $(n-r)$ things from $n$ different things $(III)$ $r\left({ }^n C_r\right)$
$(D)$ $(n-r)\left({ }^{n-1} C_{r-1}+{ }^{n-1} C_r\right)$ $(IV)$ $2^n-1-n-{ }^n C_2-\ldots-{ }^n C_r$
$(V)$ ${ }^n C_{n-r}$

The correct match is:

  • A
    $A$ $B$ $C$ $D$
    $V$ $III$ $IV$ $II$
  • B
    $A$ $B$ $C$ $D$
    $I$ $II$ $IV$ $III$
  • C
    $A$ $B$ $C$ $D$
    $V$ $III$ $I$ $II$
  • D
    $A$ $B$ $C$ $D$
    $I$ $V$ $IV$ $III$

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