We wish to select 6 persons from 8, but if th | vedclass

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(NONE) The total number of persons is $8,$ and we need to select $6$ persons.
Case $1$: Person $A$ is not selected.
If $A$ is not selected,we must c

Vedclass · Accepted Answer

$22$

Vedclass · Answer

(NONE) The total number of persons is $8,$ and we need to select $6$ persons.
Case $1$: Person $A$ is not selected.
If $A$ is not selected,we must choose $6$ persons from the remaining $7$ persons $(8 - 1 = 7)$. Since $A$ is not selected,the condition regarding $B$ is satisfied (as $B$ can be selected or not). The number of ways is $C(7, 6) = 7$.
Case $2$: Person $A$ is selected.
If $A$ is selected,then $B$ must also be selected. We have already selected $2$ persons ($A$ and $B$). We need to select $4$ more persons from the remaining $6$ persons $(8 - 2 = 6)$. The number of ways is $C(6, 4) = \frac{6!}{4!2!} = \frac{6 	imes 5}{2 	imes 1} = 15$.
However,we must check if the condition is violated. The condition is: if $A$ is chosen,$B$ must be chosen. In Case $1$,$A$ is not chosen,so the condition is not violated. In Case $2$,$A$ is chosen and $B$ is chosen,so the condition is satisfied.
Total ways $= 7 + 15 = 22$.

We wish to select $6$ persons from $8,$ but if the person $A$ is chosen,then $B$ must be chosen too. In how many ways can the selection be made?

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