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

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(D) Total persons available are $10$. We need to select $5$ persons.Given that $A$ is always included and $G, H$ are excluded.Remaining persons to cho

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$^7C_3 	imes 5!$

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(D) Total persons available are $10$. We need to select $5$ persons.Given that $A$ is always included and $G, H$ are excluded.Remaining persons to choose from are $10 - 3 = 7$ (excluding $A, G, H$).We need to select $4$ more persons from the remaining $7$ to complete the group of $5$. This can be done in $^7C_4$ ways.Since $^7C_4 = ^7C_3$,the number of ways to select the group is $^7C_3$.These $5$ persons can be arranged in a row 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 space to keep only $5$ of them. If $A$ must be included,and $G$ and $H$ must not be included in the group of $5$,in how many ways can we arrange the group in a row?

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