Question

In how many ways can 8 identical pens be distributed among Amal, Bimal, and Kamal so that Amal gets at least 1 pen, Bimal gets at least 2 pens, and Kamal gets at least 3 pens?

• A. 3
• B. 5
• C. 4
• D. 6

Answer 1

The Correct Option is D

The data is shown below.
A B K
1 2 3
The remaining 2 pens can go to different people
(3 ways – 1,1,0; 0,1,1; 1,0,1) or the same person (3 ways – 2,0,0; 0,2,0; 0,0,2).
Alternately, we can distribute the last 2 identical pens among the three of them using
x1+ x2+ x3 = 2, which has 4C2 non-negative integral solutions, i.e. 6.