Question

Find the number of ways of distributing 7 identical balls into three different boxes so that no box is empty and each box being large enough to accomodate all balls.

• A. 15
• B. $7^3$
• C. $3^7$
• D. $\frac{7!}{3!}$

Answer 1

The correct option is A 15

Equation for distributing 7 identical balls among 3 different boxes x, y and z is x + y + z = 7
Allotting one ball initially to each box, the equation reduces to x + y + z = 4
Now, Number of ways of distributing the remaining 4 identical balls among 3 different boxes
${=}^{4+3-1}{C}_{3-1}{=}^6{C}_2=15$