The total number of ways in which 5 balls of different colours can be distributed among 3 persons so that each person gets at least one ball is

Question

The total number of ways in which 5 balls of different colours can be distributed among 3 persons so that each person gets at least one ball is (A) 75 (B) 150 (C) 210 (D) 243

Tardigrade Admin · Accepted Answer

Number of ways =35- 3 C1 ⋅ 25+ 3 C2 15 =243-96+3=150

Q. The total number of ways in which 5 balls of different colours can be distributed among 3 persons so that each person gets at least one ball is

75

150

210

243

Number of ways
$= 3^{5} -^{3} C_{1} \cdot 2^{5} +^{3} C_{2} 1^{5}$
$= 243 - 96 + 3 = 150$

Q. The total number of ways in which 5 balls of different colours can be distributed among 3 persons so that each person gets at least one ball is

75

150

210

243

Number of ways =35−3C1​⋅25+3C2​15 =243−96+3=150

Number of ways
$= 3^{5} -^{3} C_{1} \cdot 2^{5} +^{3} C_{2} 1^{5}$
$= 243 - 96 + 3 = 150$