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find the number of ways 1 can put 3 balls numbered 1,2,3 in three boxes labelled a,b,c such that at the most one box is empty
We have three diff balls and three diff box . Now at most one box is empty - so there are two cases 1. None box is empty 2. One box is empty therefore , if none box is empty number of ways =3x2x1 =6 if one box is empty , we can choose that box in 3 ways and the 3 balls can be put in two boxes in 3P2 ways . so number of ways in case 2= 3x3p2= 3x6=18 therefore total number of ways = 18+6=24
We have three diff balls and three diff box .
Now at most one box is empty - so there are two cases
1. None box is empty
2. One box is empty
therefore , if none box is empty number of ways =3x2x1 =6
if one box is empty , we can choose that box in 3 ways and the 3 balls can be put in two boxes in 3P2 ways .
so number of ways in case 2= 3x3p2= 3x6=18
therefore total number of ways = 18+6=24
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