Final answer:
The number of different ways 4 boys and 3 girls can be selected from 6 boys and 10 girls is 16,800.
Step-by-step explanation:
To find the number of different ways 4 boys and 3 girls can be selected from 6 boys and 10 girls, we can use the combination formula. The number of combinations is given by the formula:
C(n, r) = n! / (r!(n-r)!)
where n is the total number of elements and r is the number of elements to be selected. In this case, n = 16 (6 boys + 10 girls) and r = 7 (4 boys + 3 girls).
Using this formula, we can calculate:
C(16, 7) = 16! / (7!(16-7)!) = 16! / (7!9!)
By simplifying the expression, we get:
C(16, 7) = (16*15*14*13*12*11*10) / (7*6*5*4*3*2*1) = 16,800