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  • A bag contains 7 different colored marbles. In how many ways can the marbles be arranged in a row such that two specific marbles are not placed together?<stron

A bag contains 7 different colored marbles. In how many ways can the marbles be arranged in a row such that two specific marbles are not placed together?

Option: 1

4200


Option: 2

2500


Option: 3

3600

 


Option: 4

4800


Answers (1)

Given that,

There are 7 different colored marbles that are placed in a bag so that 2 specific marbles shall not be together.

The number of ways in which 7 marbles can be arranged is 12! ways.

The number of ways, when 2 specific marbles are together, is given by,

6 ! \times 2 !

So, the number of ways when 2 specific marbles are not together is given by,

7 !-6 ! \times 2 !

Thus,

\begin{aligned} & 7 !-6 ! \times 2 !=5040-1440 \\ & 7 !-6 ! \times 2 !=3600 \end{aligned}

Therefore, the total number of ways for placing the marbles in the bag is 3600 ways.

Posted by

Kshitij

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