From a class of 10 boys & 6 girls , 10 students are to be selected for a competition, atleast including 4boys & 4 girls . The 2 girls who won the prizes last year should be included . In how many ways the selection can be made ?

( ans. 2478 )

Hi Swati!

At least 4 boys are to be selected from 10 boys.

At least 4 girls are to be selected from 6 girls. Among these 6 girls 2 girls won prize last year. It is given that the 2 girls who won prizes last year must to be selected. Thus, at least 2 girls are to be selected from the reaming 4 girls.

From a class of 10 boys & 6 girls, 10 students are to be selected for a competition, at least including 4 boys & 4 girls such that 2 girls who won the prizes last year should be included. This is same as selecting 8 students from a class of 10 boys & 4 girls such that at least 4 boys & 2 girls are to be selected. This can be done in the following ways.

 

(i)  2 girls and 6 boys.

(ii)  3 girls and 5 boys.

(iii)   4 girls and 4 boys.