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A family comprise of an old man,6 adults,and 4 children is to be seated in a row with the condition that children would occupy both the ends and never occupy either side if the old man.how many sitting arrangements are posdible.?
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A family comprise of an old man,6 adults,and 4 children is to be seate...
Ans.

Method to Solve :

i) There are 11 persons and 11 places
ii) Of these first 2 places has to be with children; ==> 4 x 3 = 12
Third place can only be with any one of the 6 adults = 6
Ninth place can again be with any one of the remaining 5 adults = 5
Tenth and eleventh places again has to be with children = 2 x 1 = 2
The remaining 5 places can be with 4 adults and one old man = 5! = 120

Thus total permutation = 12 x 6 x 120 x 5 x 2 = 86400

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A family comprise of an old man,6 adults,and 4 children is to be seate...
Arranging the Family Members in a Row
- There are 6 adults, 4 children, and 1 old man in the family.
- The children must occupy both ends of the row.
- The old man cannot sit next to any child.

Arranging the Children
- Since the children must occupy both ends, there are 2 ways to arrange them.
- The children can be arranged in 2! = 2 ways.

Arranging the Adults and Old Man
- After fixing the children at the ends, there are 7 positions left for the 6 adults and the old man.
- The old man cannot sit next to any child, so he must occupy a position between two adults.
- There are 6 ways to choose the position for the old man.
- After placing the old man, the remaining 6 adults can be arranged in 6! ways.

Calculating the Total Arrangements
- The total number of arrangements is given by: 2! * 6 * 6!
- 2! = 2 ways to arrange the children
- 6 = 6 ways to choose the position for the old man
- 6! = 720 ways to arrange the 6 adults
- Therefore, the total number of possible sitting arrangements is 2 * 6 * 720 = 8640.
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A family comprise of an old man,6 adults,and 4 children is to be seated in a row with the condition that children would occupy both the ends and never occupy either side if the old man.how many sitting arrangements are posdible.?
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