Question

Number of ways in which 6 different objects can be distributed among 3 persons such that each one receives atleast one object is equal to

• A. $108$
• B. $240$
• C. $360$
• D. $540$

Answer 1

The correct option is D $540$

The different ways are :

$(1,1,4)$

$(1,2,3)$

$(2,2,2)$

No. of ways for each case ${}^6{C}_1\times {}^5{C}_1\times {}^4{C}_4$

or ${}^6{C}_1\times {}^5{C}_2\times {}^3{C}_3$

or ${}^6{C}_2\times {}^4{C}_2\times {}^2{C}_2$

or $30$ in $1st$ case, $60$ in $2nd$, $90$ in $3rd$ and for each case selection is distributed in $3,6,1$ way respectively.

$\therefore$ total no. of ways $30\times 3+60\times 6+90\times 1=540$

Hence, the answer is $540.$