Advertisement Remove all ads

In a Group of 6 Boys and 4 Girls, Four Children Are to Be Selected. in How Many Different Ways Can They Be Selected Such that at Least One Boy Should Be There? - Mathematics

Advertisement Remove all ads
Advertisement Remove all ads
MCQ

In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?

Options

  • 159

  • 194

  • 205

  • 209

Advertisement Remove all ads

Solution

209
Explanation:

We may have (1 boy and 3 girls) or (2 boys and 2 girls) or (3 boys and 1 girl) or (4 boys).
∴ Required number

= `(""^6C_1xx""^4C_3)+(""^6C_2xx""^4C_2)+(""^6C_3xx""^4C_1)+(""^6C_4)`

= `(6xx4)+((6xx5)/(2xx1)xx(4xx3)/(2xx1))+((6xx5xx4)/(3xx2xx1)xx4)+((6xx5)/(2xx1))`

= (24 + 90 + 80 + 15)

= 209

Concept: Permutation and Combination (Entrance Exam)
  Is there an error in this question or solution?
Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×