Question

There are 3 boxes and 6 balls. In how many ways these balls can be distributed if all the balls and all the boxes are different ?

Answer 1

6^3

Step-by-step explanation:

Since there is no restriction given so many no of balls can go in any box

since there are 3 boxes and in each box 6 balls can come

so total no of ways= 6×6×6

= 216

Answer 2

Answer:

$540$ ways these balls can be distributed if all the balls and all the boxes are different

Step-by-step explanation:

Each ball has 3 choices. Hence the total number of ways of distribution $=3 \times 3 \times 3 \times 3 \times 3 \times 3=3^{6}$

But this includes two cases

(i) One box is empty.

(ii) Two boxes are empty.

The no. of ways in which this happens$=3\left(2^{6}-1\right)$

Hence the reqd. no. $=3^{6}-3\left(2^{6}-1\right)$

$=729-3 \times 63=729--189 \\\\=540$