Question

In a group of 6 boys and 8 girls, 5 students have to be selected. In how many ways it can be done so that at least 2 boys are included

Answer 1

Please see the attachment

Answer 2

Answer: 1526

Step-by-step explanation:

Number of boys = 6

Number of girls= 8

Now we have to find the number of ways  so that at least 2 boys are included

Let 2 boys includes then number of ways

$_{2}^{6}\textrm{C}\times _{3}^{8}\textrm{C}=840$

Let 3 boys includes

$_{3}^{6}\textrm{C}\times _{2}^{8}\textrm{C}=560$

Let 4 boys included

$_{4}^{6}\textrm{C}\times _{1}^{8}\textrm{C}=120$

Let 5 boys included

$_{5}^{6}\textrm{C}=6$

Hence the total ways are $_{2}^{6}\textrm{C}\times _{3}^{8}\textrm{C}+_{3}^{6}\textrm{C}\times _{2}^{8}\textrm{C}+_{4}^{6}\textrm{C}\times _{1}^{8}\textrm{C}+_{5}^{6}\textrm{C}$= 1526