một đội học sinh giỏi của trường THPT gồm 6 học sinh khối 12 5 học sinh khối 11 4 học sinh khối 10 số cách chọn 3 học sinh trong đó mỗi khối có một em

To solve this problem, we can use the concept of combinations. The total number of ways to choose 3 students, one from each grade, can be calculated using the combination formula. The number of ways to choose 3 students, one from each grade, is given by: \[\binom{6}{1} \times \binom{5}{1} \times \binom{4}{1}\] Where: - \(\binom{n}{r}\) represents the number of ways to choose r items from n distinct items without considering the order. Using the combination formula: \[\binom{n}{r} = \frac{n!}{r!(n-r)!}\] We can calculate the total number of ways as follows: \[\binom{6}{1} = \frac{6!}{1!(6-1)!} = 6\] \[\binom{5}{1} = \frac{5!}{1!(5-1)!} = 5\] \[\binom{4}{1} = \frac{4!}{1!(4-1)!} = 4\] So, the total number of ways to choose 3 students, one from each grade, is: \[6 \times 5 \times 4 = 120\] Therefore, there are a total of 120 ways to choose 3 students with one student from each grade.