Question
Question: 15 identical balls have to be put in 5 different boxes. Each box can contain any number of balls. To...
15 identical balls have to be put in 5 different boxes. Each box can contain any number of balls. Total number of ways of putting the balls into box so that each box contains at least 2 balls, is equal to-
A
9C5
B
10C5
C
6C5
D
10C6
Answer
9C5
Explanation
Solution
Let the balls put in the box are x1, x2, x3, x4 and x5.
We must have x1 + x2 + x3 + x4 + x5 = 15, xi ³ 2
Ž (x1 – 2) + (x2 – 2) + (x3 – 2) + (x4 – 2) + (x5 – 2) = 5
Ž y1 + y2 + y3 + y4 + y5 = 5, yi = xi – 2 ³ 0
= 5+5–1C5 = 9C5 .