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Question
A business man hosts a dinner to 21 guests. He is having 2 round tables which can accommodate 15 and 6 persons each. In how many ways can he arrange the guests?
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Solution
A businessman hosts a dinner for 21 guests.
15 people can be accommodated at one table in 21C15 ways. They can arrange themselves in \[\left( 15 - 1 \right)! = 14!\]ways.
The remaining 6 people can be accommodated at another table in 6C6 ways. They can arrange themselves in\[\left( 6 - 1 \right)! = 5!\] ways.
∴ Total number of ways =\[{}^{21} C_{15} \times^6 C_6 \times 14! \times 5! =^{21} C_{15} \times 14! \times 5!\]
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