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Question Number 134232 by liberty last updated on 01/Mar/21

$$ \\ $$ In how many ways can 5 men, 4 women, and 3 children be arranged in a row of 12 seats if the children sit together?\\n

Answered by mr W last updated on 01/Mar/21

10!3!=21 772 800

$$\mathrm{10}!\mathrm{3}!=\mathrm{21}\:\mathrm{772}\:\mathrm{800} \\ $$

Answered by Ñï= last updated on 01/Mar/21

MMMMCCC_(take as 1 people) WWMWW  all 10 people  A_(10) ^(10) ×A_3 ^3 =10!×3!

$${MMMM}\underset{{take}\:{as}\:\mathrm{1}\:{people}} {\underbrace{{CCC}}WWMWW} \\ $$ $${all}\:\mathrm{10}\:{people} \\ $$ $${A}_{\mathrm{10}} ^{\mathrm{10}} ×{A}_{\mathrm{3}} ^{\mathrm{3}} =\mathrm{10}!×\mathrm{3}! \\ $$

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