There are 10 persons named A, B, dots, J. We | vedclass

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(D) Total persons available are $10$. We need to form a team of $5$ and arrange them in a line.Since $A$ must be included,we have $1$ spot filled by $

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$^7C_3 	imes 5!$

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(D) Total persons available are $10$. We need to form a team of $5$ and arrange them in a line.Since $A$ must be included,we have $1$ spot filled by $A$,leaving $4$ spots to be filled.Since $G$ and $H$ must not be included,we exclude them from the remaining $9$ people,leaving $7$ people to choose from.We need to select $4$ people from the remaining $7$,which can be done in $^7C_4$ ways.Since $^7C_4 = ^7C_3$,the number of ways to select the team is $^7C_3$.Once the $5$ members are selected (including $A$),they can be arranged in a line in $5!$ ways.Therefore,the total number of arrangements is $^7C_3 	imes 5!$.

There are $10$ persons named $A, B, \dots, J$. We have the capacity to accommodate only $5$. In how many ways can we arrange them in a line if $A$ must be included,and $G$ and $H$ must not be included in the team of $5$?

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