The number of ways in which 6 distinct things | vedclass

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(C) Each of the $6$ distinct objects can be placed in either of the $2$ boxes in $2$ ways. Since there are $6$ objects,the total number of ways to dis

Vedclass · Accepted Answer

$62$

Vedclass · Answer

(C) Each of the $6$ distinct objects can be placed in either of the $2$ boxes in $2$ ways. Since there are $6$ objects,the total number of ways to distribute them is $2^6 = 64$. However,this includes the $2$ cases where one of the boxes remains empty (i.e.,all $6$ objects are in the first box,or all $6$ objects are in the second box). Since the condition is that no box is empty,we subtract these $2$ cases. Required number of ways $= 2^6 - 2 = 64 - 2 = 62$.

The number of ways in which $6$ distinct things can be distributed into $2$ boxes so that no box is empty is

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