Question

If 6 object are distributed at random among 6 persons, the probability that atleast one of them will not get anything is

• A. 6(6!)
• B. $\frac{5^6}{6!}$
  
• C. $\frac{6^6-6!}{6^6}$
  
• D. none of these.

Answer 1

The correct option is C $\frac{6^6-6!}{6^6}$


6 objects can be distributed among 6 persons in $6^6$ ways

$\therefore$ Total number of ways=$6^6$

The number of ways of distribution in which each one gets only thing is 6!. So, the number at distribution in which atleast one of them does not get anything $6^6-6!$
Hence, required probability=$\frac{6^6-6!}{6^6}$