There are 6 balls of different colours and 3 boxes of different sizes. Each box can hold all the six balls. The balls are put in the boxes so that no box remains empty. The number of ways this can be done is

Question

There are 6 balls of different colours and 3 boxes of different sizes. Each box can hold all the six balls. The balls are put in the boxes so that no box remains empty. The number of ways this can be done is (A) 534 (B) 543 (C) 540 (D) 28

Tardigrade Admin · Accepted Answer

Each ball has 3 choices. Hence the total number of ways of distribution =3×3×3×3×3×3=36 But this includes two cases (i) One box is empty. (ii) Two boxes are empty. The no. of ways in which this happens = 3(26-1) Hence the reqd. no. =36-3(26-1) =729-3 × 63=729--189 =540

Q. There are $6$ balls of different colours and $3$ boxes of different sizes. Each box can hold all the six balls. The balls are put in the boxes so that no box remains empty. The number of ways this can be done is

$534$

$543$

$540$

$28$

Q. There are 6 balls of different colours and 3 boxes of different sizes. Each box can hold all the six balls. The balls are put in the boxes so that no box remains empty. The number of ways this can be done is

534

543

540

28

Each ball has 3 choices. Hence the total number of ways of distribution =3×3×3×3×3×3=36 But this includes two cases (i) One box is empty. (ii) Two boxes are empty. The no. of ways in which this happens = 3(26−1) Hence the reqd. no. =36−3(26−1) =729−3×63=729−−189 =540

Q. There are $6$ balls of different colours and $3$ boxes of different sizes. Each box can hold all the six balls. The balls are put in the boxes so that no box remains empty. The number of ways this can be done is

$534$

$543$

$540$

$28$