Out of 100 students,two sections of 40 and 60 | vedclass

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Question

(A) Let the two sections be $S_1$ (size $40$) and $S_2$ (size $60$).Total ways to place $2$ specific students into these sections is the total number

Vedclass · Accepted Answer

$\frac{16}{33}$

Vedclass · Answer

(A) Let the two sections be $S_1$ (size $40$) and $S_2$ (size $60$).Total ways to place $2$ specific students into these sections is the total number of ways to choose $2$ spots out of $100$ for them,which is $100 	imes 99$.Alternatively,consider the probability that both are in the same section.Probability both are in $S_1 = \frac{40}{100} 	imes \frac{39}{99} = \frac{2}{5} 	imes \frac{13}{33} = \frac{26}{165}$.Probability both are in $S_2 = \frac{60}{100} 	imes \frac{59}{99} = \frac{3}{5} 	imes \frac{59}{99} = \frac{59}{165}$.Probability both are in the same section $= \frac{26}{165} + \frac{59}{165} = \frac{85}{165} = \frac{17}{33}$.Probability both are in different sections $= 1 - \frac{17}{33} = \frac{16}{33}$.

Out of $100$ students,two sections of $40$ and $60$ are formed. If you and your friend are among the $100$ students,what is the probability that you both enter different sections?

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