Q. 74.5( 6 Votes )

From a class of 12 boys and 10 girls, 10 students are to be chosen for the competition, at least including 4 boys and 4 girls. The 2 girls who won the prizes last year should be included. In how many ways can the selection be made?

Answer :

Given that 10 students need to be selected from 12 boys and 10 girls including at least 4 boys and 4 girls.


It is also told that the two girls must be includes who won prizes last year.


The cases that satisfy these conditions are:


i. Selecting 6 boys and 4 girls (in which 2 girls are already included)


ii. Selecting 5 boys and 5 girls (in which 2 girls are already included)


iii. Selecting 4 boys and 6 girls. (in which 2 girls are already included)


Let us assume the total no. of ways of selection be N,


N = (no. of ways of selecting 6 boys and 2 girls from remaining 12 boys and 8 girls) + (no. of ways of selecting 5 boys and 3 girls from remaining 12 boys and 8 girls) + (no. of ways of selecting 4 boys and 4 girls from remaining 12 boys and 8 girls)


Since, two girls are already selected,


N = (12C6 × 8C2) + (12C5 × 8C3) + (12C4 × 8C4)


We know that


And also n! = (n)(n – 1)(n – 2)…………2.1





N = (924 × 28) + (792 × 56) + (495 × 70)


N = 25872 + 44352 + 34650


N = 104874


The total number of ways of product is 11 ways.


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