A class has fifteen boys and five girls. Suppose three students are selected at random from the class. The probability that there are two boys and one girl is

Question

A class has fifteen boys and five girls. Suppose three students are selected at random from the class. The probability that there are two boys and one girl is (A) (35/76) (B) (35/38) (C) (7/76) (D) (35/72)

Tardigrade Admin · Accepted Answer

∴ Required probability =( 15 C2 × 5 C1/ 20 C3) =(15 × 7 × 5/(20 × 19 × 18)3 × 2) =(7 × 25/20 × 19)=(35/76)

Q. A class has fifteen boys and five girls. Suppose three students are selected at random from the class. The probability that there are two boys and one girl is

$\frac{35}{76}$

$\frac{35}{38}$

$\frac{7}{76}$

$\frac{35}{72}$

$∴$ Required probability $= \frac{^{15} C _{2} \times ^{5} C _{1}}{^{20} C _{3}}$
$= \frac{15 \times 7 \times 5}{\frac{20 \times 19 \times 18}{3 \times 2}}$
$= \frac{7 \times 25}{20 \times 19} = \frac{35}{76}$

Q. A class has fifteen boys and five girls. Suppose three students are selected at random from the class. The probability that there are two boys and one girl is

7635​

3835​

767​

7235​

∴ Required probability =20C3​15C2​×5C1​​ =3×220×19×18​15×7×5​ =20×197×25​=7635​

$\frac{35}{76}$

$\frac{35}{38}$

$\frac{7}{76}$

$\frac{35}{72}$

$∴$ Required probability $= \frac{^{15} C _{2} \times ^{5} C _{1}}{^{20} C _{3}}$
$= \frac{15 \times 7 \times 5}{\frac{20 \times 19 \times 18}{3 \times 2}}$
$= \frac{7 \times 25}{20 \times 19} = \frac{35}{76}$