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In an assembly of 10 scholars,3 are mathematicians and 3 physicists.There are 2 rows, each containing 5 chairs and all mathematicians will sit in one row and physicists in the other, the remaining scholars are to be seated in the vacant positions left.In how many ways can they be seated?Plz explain the reason.

In an assembly of 10 scholars,3 are mathematicians and 3 physicists.There are 2 rows, each containing 5 chairs and all mathematicians will sit in one row and physicists in the other, the remaining scholars are to be seated in the vacant positions left.In how many ways can they be seated?Plz explain the reason.

Grade:12

2 Answers

akshay choudhary
15 Points
10 years ago

144 ways.becoj 3 mathematician are to be seated in i row there are 5 chars so totl no of ways 6o.this will be same for physiscits.and remaining for sckolars will be seated in four vacant places so no of ways 24.so  THE TOTL NO OF WAYS 144

Ashwin Muralidharan IIT Madras
290 Points
10 years ago

Hi Ashmita,

 

Permutations and Combinations is the topic in Mathematics, where one needs to be absolutely clear in the concepts of the topic.

 

Here please note, we can arrange the Mathematicians, and the Physicists, and the remaining Scholars (the and would tell you that you would have to multiply the number of individual ways).

(And also note that, the Mathematicians, and Physicists can be in any one of the two rows).

 

So Here, the number of ways would be: 2*60*60*24.

where 2 corresponds to Mathematicians being in either of the two rows (and once Mathematicians go to one row, the physicists automatically go to the other row).

60 corresponds to the number of ways where 3 Mathmaticians can be seated in a row containing 5 seats (which is 5P3).

other 60 corresponds to the Physicists.

And the remaining 4 can be seated in 4! (=24) ways.

 

So Answer: 2*60*60*24 = 172800 ways.

 

Have also posted answers to you previous Physics Questions (On Newton's Laws and Pulleys). Do have a look at them as well.

 

Hope that helps,

All the best,

Regards,

Ashwin (IIT Madras).

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