Chapter 12, Problem 12.1VP

Interpretation Introduction

To find:

The number of arrangements of the marbles possible before and after removal of the divider in the (a) block in the (b) block.

Answer to Problem 12.1VP

Solution:

Only one arrangement is possible for (a) block before removing the divider. After removal of the divider, three arrangements are possible.

There are two possible arrangements of the marbles for (b) block before removal of divider and six possible arrangements after removal of the divider.

Explanation of Solution

For (a) block:

Only one possible arrangement is possible before removal of the divider which is RRE.

After the divider is removed, the marbles can be arranged in three ways as:

RRE

ERR

RER

For (b) block:

Only two arrangements are possible before removal of the divider, which are BRE and RBE.

After the removal of the divider, four arrangements are:

BRE, RBE

EBR, ERB

BER, REB

Where, R, B, and E represent red marble, blue marble and empty depression respectively.

Conclusion:

Before removal of the divider, there is only one possible arrangement for (a) block and two for (b) block.

After removal of the divider, three arrangements of the marbles are possible for (a) block and six arrangements possible for (b) block.