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
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
Share
Notifications

View all notifications


      Forgot password?
View in app×