a teacher must select 2 students from a list of 4 students. How many distinct groups of 2 students are possible?

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This is a combination problem. We need to select 2 students from 4 students, where the order doesn't matter. We have 4 students labeled S1, S2, S3, and S4. We need to find how many different groups of 2 students we can form. Since the order of selection doesn't matter, this is a combination problem. We use the combination formula: C of n choose k equals n factorial divided by k factorial times n minus k factorial. For our problem, n equals 4 and k equals 2, so we substitute to get C of 4 choose 2 equals 4 factorial divided by 2 factorial times 2 factorial. Now let's calculate the factorials step by step. 4 factorial equals 4 times 3 times 2 times 1, which equals 24. 2 factorial equals 2 times 1, which equals 2. Substituting back into our formula: C of 4 choose 2 equals 24 divided by 2 times 2, which equals 24 divided by 4, which equals 6. Let's verify our answer by listing all possible groups. We can form: Group 1 with S1 and S2, Group 2 with S1 and S3, Group 3 with S1 and S4, Group 4 with S2 and S3, Group 5 with S2 and S4, and Group 6 with S3 and S4. This gives us exactly 6 distinct groups, confirming our calculation. In conclusion, when a teacher must select 2 students from a list of 4 students, there are 6 distinct groups possible. We solved this using the combination formula C of 4 choose 2, which equals 4 factorial divided by 2 factorial times 2 factorial, giving us 24 divided by 4, which equals 6. The answer is 6 distinct groups.