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There are unlimited number of identical bal s of our different colours. How many ar rangements of atmost 6 balls can be made by using them ? [to be arr anged in a single row only] (a) 1365 (b) 2730 (c) 5460 (d) None of the above

 There are unlimited number of identical bal s of our different colours. How many ar rangements of atmost 6
balls can be made by using them ? [to be arr anged in a single row only]
(a) 1365 (b) 2730 (c) 5460 (d) None of the above

Grade:12

1 Answers

Arun
25763 Points
one year ago
There is an unlimited number of identical of three rows.
 
Number of arrangement of 7 balls in a row =3 
7
 
 
Number of arrangement of 6 balls in a row =3 
6
 
 
Number of arrangement of 5 balls in a row =3 
5
 
 
Number of arrangement of 4 balls in a row =3 
4
 
 
Number of arrangement of 3 balls in a row =3 
3
 
 
Number of arrangement of 2 balls in a row =3 
2
 
 
Number of arrangement of 1 balls in a row =3
 
∴ Number of arrangement of almost 7 balls in row that can be made (n)=3+3 
2
 +3 
3
 +3 
4
 +3 
5
 +3 
6
 +3 
7
 
 
As it is in GP
 
n= 
3−1
3(3 
7
 −1)
​ 
 
 
2
3
​ 
 (2187−1)
 
2
3
​ 
 ×2186
 
=3×1093
 
n=3279

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