Question

A boy contains 5 pink , 3 blue & 6 black ball. How many solution of ball can be formed by taking at least one ball form the boy
1. 157 
2. 187
3. 167 
4. 197 
5. 177

Answer 1

Correct Answer - Option 3 : 167 

Given

Number of pink balls = 5

Number of blue balls = 3

Number of black balls = 6

Concept

Number of ways to select one or more things out of ( x + y + z) things where x are of same type, y are if same type and z are of same type, then number of ways are (x + 1) (y + 1) (z + 1) – 1

Calculation

Here x = 5, y = 3 and z = 6

⇒ (5 + 1) (3 + 1) (6 + 1) – 1

⇒ (6 × 4 × 7) – 1

⇒ 168 – 1

⇒ 167