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

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(D) Total persons available = $10$ $(A, B, C, D, E, F, G, H, I, J)$.We need to form a team of $5$ persons.Condition $1$: $A$ must be included.Conditio

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$^7C_3 	imes 5!$

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(D) Total persons available = $10$ $(A, B, C, D, E, F, G, H, I, J)$.We need to form a team of $5$ persons.Condition $1$: $A$ must be included.Condition $2$: $G$ and $H$ must not be included.Since $A$ is already selected, we need to select $4$ more persons from the remaining $10 - 3 = 7$ persons (excluding $A, G, H$).Number of ways to select $4$ persons from $7$ is $^7C_4$.Since $^7C_4 = ^7C_3$, the selection can be done in $^7C_3$ ways.Now, we have a team of $5$ persons (including $A$). These $5$ persons 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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