Q24 of 31 Page 7

A group consists of 5 girls and 8 boys. In how many ways can a team of 5 members be selected if a team has:

(i) no girl (ii) at least 3 girls (iii) at least one girl and one boy

(i) no girl


As there are 5 girls and 8 boys in the group.


No girl means that team will only have boys.


As team needs 5 members. So, the number of ways 5 boys can be selected from 8 boys is:


5C0 × 8C5





= 336 ways


(ii) at least 3 girls


There can be following cases:


Case 1: 3 girls,2 boys


5C3 × 8C2





= 10× 28


= 280 ways


Case 2: 4 girls,1 boy


5C4 × 8C1





= 5× 8


= 40 ways


Case 2: 5 girls,0 boy


5C5 × 8C0





= 1


So total ways = 280+ 40+1


= 321 ways


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