Question

In a snooker game round five balls of different colours are to be sent in three holes of different sizes. each hole can hold all five balls. the number of ways in which we can place the bails in the holes so that no hole remains empty is?

A. 19
B. 180
C. 150
D. 60

Answer 1

There are 150 ways to distribute the five balls into three non-empty holes in the snooker game round.

Since each hole can hold all five balls, the question translates to finding the number of ways to distribute five distinct balls into three non-empty groups.

There are two possible scenarios for distributing the balls:

Scenario 1:

One hole gets three balls, and the remaining two holes get one ball each.

Choose 3 balls out of 5:

• ⁵C₃ ways

Distribute the remaining 2 balls into the other two holes: 2!ways (since order doesn't matter)

• Total ways ⁵C₃ * 2! = 60

Scenario 2: Two holes get two balls each, and the remaining hole gets one ball.

Choose 2 balls out of 5: ⁵C₂ ways

Choose one hole to receive the remaining 3 balls: 3 ways

Distribute the 2 chosen balls into the other two holes: 2! ways (order doesn't matter)

Total ways : ⁵C₂ * 3 * 2! = 90

The total number of ways to distribute the balls so that no hole remains empty is:

Total ways = 60 + 90 = 150

So, there are 150 ways to distribute the five balls into three non-empty holes in the snooker game round.