Q78 / 160 · AP EAMCET 2023 (16 May Shift 1) · Mathematics

From out of 100 enrolled students, two sections of strength 40 and 60 are formed. If you and your friend are among those 100 students, then the probability that both of you are placed in the same section is

  • A
    $\frac{{ }^{98} \mathrm{C}_{40}+{ }^{98} \mathrm{C}_{58}}{{ }^{100} \mathrm{C}_{40}}$
  • Correct answer
    B
    $\frac{{ }^{40} \mathrm{C}_2+{ }^{60} \mathrm{C}_2}{{ }^{100} \mathrm{C}_2}$
  • C
    $\frac{{ }^{98} \mathrm{C}_{60}+{ }^{98} \mathrm{C}_{38}}{{ }^{100} \mathrm{C}_{60}}$
  • D
    $\frac{{ }^{98} \mathrm{C}_{58}+{ }^{98} \mathrm{C}_0}{{ }^{100} \mathrm{C}_2}$

Solution

Total no. of ways of selecting 2 students out of 100 $={ }^{100} C_2$ No. of ways in which both of us enter the same section $={ }^{40} C_2+{ }^{60} C_2$ $\therefore$ Required probability $=\frac{{ }^{40} C_2+{ }^{60} C_2}{{ }^{100} C_2}$

Hence, the correct answer is option: 'B'.

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