Question

A box filled with more than 100 balls contains balls of blue, green, red, and orange color. In how many ways, Chakrabir can select 7 balls out of the box if it is known that the box has at least 7 balls of each color?

1. 120
2. 136
3. 128
4. 144

Answer 1

Correct Answer - Option 1 : 120

Calculation:

⇒ Suppose the number of blue balls selected = A

⇒ The number of green balls selected = B

⇒ The number of red balls selected = C

and the number of orange balls selected = D

⇒ Now, the problem is simplified to the number of non-negative integral solution of the equation

⇒ A + B + C + D = 7

⇒ Which is given by (n + r - 1)C_(r  - 1)

⇒ Here n = 7 and r = 4

⇒ Hence,¹⁰C₃ = 120

⇒ The total number of ways in which n identical items can be distributed among p persons so that each person may get any number of items is ^n+p-1Cp-1.

⇒ Total number of ways in which n identical items can be distributed among p persons such that each of them receives at least one item ^n-1Cp-1