A probability problem by Suhaas Shukla

Probability Level 4

A family consist of a grandfather, 5 children 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:

The answer is 19353600.

2 solutions

Smarth Mittal
Jan 24, 2015

There are a total of 14 seats.

_ _ _ _ _ _ _ _ _ _ _ _ _ _

Now, The grandchildren will occupy 4 seats on either side and hence their total number of arrangements are 8!

Since the grandfather will not sit on either side of grandchildren. Therefore onnly 4 places are left out for him and obviously he can occupy only one. Hence his arrangements are 4c1 which is equal to 4

Now, there are 5 children and hence can be arranged in 5! ways.

Hence the total number of ways are:-

8! * 5! * 4 = 19353600

I could not figure out how to do this one

Charlotte Milanese - 4 years, 5 months ago

Suhaas Shukla
Sep 3, 2014

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=19353600

You should give options.In my method Calculation error occured

D K - 2 years, 10 months ago

A probability problem by Suhaas Shukla

The answer is 19353600.

2 solutions

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