From a class of 10 boys and 6 girls , 10 students are to be selected for a competition , atleast including 4 boys and 4 girls , the two girls who won the prizes last years should be included , in how many ways the selection can be made?
Answers
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:
The total number of boys = 12
The total number of girls = 10
The total number of girls for the competition = 10 + 2 = 12
The number of ways = (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)
Here, two girls are already selected, = (12C6 × 8C2) + (12C5 × 8C3) + (12C4 × 8C4)
On using the formula, nCr = n!/r!(n – r)! = (924 × 28) + (792 × 56) + (495 × 70) = 25872 + 44352 + 34650 = 104874
Thus, the total number of ways of product is 104874.