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Binomial Theorem — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSBinomial Theorem3 Marks
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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Answer

In One round table the business man can accommodate the guests in ways. In the second round table he can the guests in ways. Keeping one guest as fixed in the round table, the other 14 guests can be arrange in 14! ways. Keeping one guest as fixed in the second round tabie, the other 5 guests can be number of ways in which the guests can be arrange is $={^\text{21}}\text{C}_{\text{15}}\times{^\text{6}}\text{C}_{\text{6}}\times14!\times5!\ \text{ways}$

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