Permutation-Combination
Aptitude

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Q.

A family consist of a grandfather, $5$ sons and daughter and $8$ grandchildren.

They are to be seated in a row for dinner. The grandchildren wish to occupy the $4$ seats at each end and the grandfather refuses to have a grandchild on either side of him.

The number of ways in which the family can be made to sit is:

 A.

21530

 B.

8! × 480

 C.

8! × 360

 D.

8! × 240

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Solution:
Option(B) is correct

Total no. of seats:

$= 1$ grandfather $+ 5$ sons and daughters $+ 8$ grandchildren

$= 14.$

The grandchildren can occupy the $4$ seats on either side of the table in $4! = 24$ ways.

The grandfather can occupy a seat in $(5-1)= 4$ ways ($4$ gaps between $5$ sons and daughter).

And, the remaining seats can be occupied in $5!= 120$ ways ($5$ seat for sons and daughter).

Hence total number of required ways $= 8! × 480$


(8) Comment(s)


ABHIJEET
 ()

Admin correct the typo in the question.. 5 sons and daughter implies 5 sons and a daughter...people use this site for improving their quant abilities..maybe u should brush up your verbal abilities first..change it to 5 sons and a daughter to just 5 sons or whatever that doesn't mess up



Aayush
 ()

if we goes this way

4 grandchildren occupy corner sit=4!=24 ways

now 10 seats are remaining and grandfather refuse to sit near grandchildren hence (10-4)=6 seats hence 6 ways for grandfather

now remaining seats are 9 in which 7 seats for remaining 4 grandchildren no. of ways = 7C4*4!

now 5 sons and daughter can be arranged as = 5!=120

total ans should come = 24*6*7C4*4!*120 = 8!*360

can anyone explain this.



Chakarya
 ()

If there are only 5 number of sons and daughters on whole, why did they mention 5 SonS and DAUGHTER instead of DAUGHTERS? We have a plural for sons n singular in daughter. This clearly implies 5 sons + one daughter. Total 15!!! Kindly give questions correctly



Prashanth
 ()

how 8! comes and where 24ways used in calculation??


Abhishek
 ()

consider this 8C4 * 4! * 4!. :)


Madhav
 ()

5 sons and daugter means $5 s+ 1 d=6$, is it write or wrong


Lohit
 ()

Question says 5 sons and daughter which means TOTAL number of sons AND daughters is 5 or there are 5 children. Had it been 5 sons and a daughter you could have said totald children are 6 (5 s+ 1 d=6)

RAKESH
 ()

its right and here total son's are 5 and one daughter