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A Tea Party is Arranged for 16 Persons Along Two Sides of a Long Table with 8 Chairs on Each Side. Four Persons Wish to Sit on One Particular Side and Two on the Other Side. in How Many Ways Can - Mathematics

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प्रश्न

A tea party is arranged for 16 persons along two sides of a long table with 8 chairs on each side. Four persons wish to sit on one particular side and two on the other side. In how many ways can they be seated?

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उत्तर

A tea party is arranged for 16 people along two sides of a long table with 8 chairs on each side.
4 people wish to sit on side \[A\]  (say) and two on side

\[B\](say).
Now, 10 people are left, out of which 4 people can be selected for side \[A\] in 10C4 ways.
And, from the remaining people, 6 people can be selected for side B in 6C6 ways.
∴ Number of selections  = \[{}^{10} C_4 \times {}^6 C_6\]
Now, 8 people on each side can be arranged in \[8!\]ways.
∴ Total number ways in which the people can be seated  =
\[{}^{10} C_4 \times {}^6 C_6 \times 8! \times 8! = {10}_{C_4} \times \left( 8! \right)^2\]
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अध्याय 17: Combinations - Exercise 17.3 [पृष्ठ २३]

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आरडी शर्मा Mathematics [English] Class 11
अध्याय 17 Combinations
Exercise 17.3 | Q 11 | पृष्ठ २३

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