Final answer:
The total number of possible committees formed from 3 boys out of 5 and 4 girls out of 6 is 150, using the combination formula.
Step-by-step explanation:
The question asks how many committees are possible when forming a committee of 3 boys and 4 girls from a group of five boys and six girls. This is a combinatorics problem, which falls under the topic of probability and statistics in mathematics. To solve it, we use the combination formula: C(n, r) = n! / [r!(n-r)!], where 'n' is the total number of items, 'r' is the number of items to choose, and '!' denotes factorial. The problem requires us to calculate two separate combinations (one for boys and one for girls) and then multiply them together to find the total number of possible committees.
For boys, we have the combination C(5, 3) because we are choosing 3 boys from 5. For girls, we have the combination C(6, 4) because we are choosing 4 girls from 6. Multiplying these two combinations together gives us the total number of unique committees that can be formed:
- Number of ways to select 3 boys = C(5, 3) = 5! / (3! * (5-3)!) = 10
- Number of ways to select 4 girls = C(6, 4) = 6! / (4! * (6-4)!) = 15
Thus, the total number of possible committees = 10 * 15 = 150.