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

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Question

(A) Total number of ways to place $2$ specific students (you and your friend) into two sections of $40$ and $60$ is equivalent to choosing $2$ spots o

Vedclass · Accepted Answer

$17$

Vedclass · Answer

(A) Total number of ways to place $2$ specific students (you and your friend) into two sections of $40$ and $60$ is equivalent to choosing $2$ spots out of $100$ for the two of you,which is $^{100}C_{2}$.The two of you will be in the same section if both are in the section of $40$ or both are in the section of $60$.Number of ways to be in the same section $= ^{40}C_{2} + ^{60}C_{2}$.Probability $= \frac{^{40}C_{2} + ^{60}C_{2}}{^{100}C_{2}}$.$= \frac{\frac{40 	imes 39}{2} + \frac{60 	imes 59}{2}}{\frac{100 	imes 99}{2}} = \frac{1560 + 3540}{9900} = \frac{5100}{9900} = \frac{51}{99} = \frac{17}{33}$.

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 the same section (in $/33$)?

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