The homework for English class was to write a poem. The teacher wants to ask 4 students, 2 boys and 2 sirls, to read their poems for the class. If there are 10 boys and 15 girls, how many different combinations of 2 boys and 2 girls can the teacher select?

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Boys Combination Calculation: To find the number of combinations of 2 boys out of 10, we use the combination formula C(n, k) = n! / (k!(n-k)!), where n is the total number of items, k is the number of items to choose, and ! denotes factorial. For 2 boys out of 10, the calculation is C(10, 2) = 10! / (2!(10-2)!).Boys Combination Result: Calculating C(10, 2) gives us 10! / (2! * 8!) = (10 * 9) / (2 * 1) = 45. There are 45 different ways to choose 2 boys out of 10.Girls Combination Calculation: Next, we find the number of combinations of 2 girls out of 15 using the same combination formula. For 2 girls out of 15, the calculation is C(15, 2) = 15! / (2!(15-2)!).Girls Combination Result: Calculating C(15, 2) gives us 15! / (2! * 13!) = (15 * 14) / (2 * 1) = 105. There are 105 different ways to choose 2 girls out of 15.Total Combinations Calculation: To find the total number of combinations of 2 boys and 2 girls, we multiply the number of combinations for boys by the number of combinations for girls. The calculation is 45 * 105.Total Combinations Result: Calculating 45 * 105 gives us 4725. There are 4725 different combinations of 2 boys and 2 girls that the teacher can select.

The homework for English class was to write a poem. The teacher wants to ask $4$ students, $2$ boys and $2$ sirls, to read their poems for the class. If there are $10$ boys and $15$ girls, how many different combinations of $2$ boys and $2$ girls can the teacher select?

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The homework for English class was to write a poem. The teacher wants to ask $4$ students, $2$ boys and $2$ sirls, to read their poems for the class. If there are $10$ boys and $15$ girls, how many different combinations of $2$ boys and $2$ girls can the teacher select?