Question: In how many ways can 6 people be divided into 2 groups of 3?
Options:
20
30
10
15
Correct Answer: 20
Solution:
The number of ways to divide 6 people into 2 groups of 3 is 6! / (3! * 3! * 2!) = 20.
In how many ways can 6 people be divided into 2 groups of 3?
Practice Questions
Q1
In how many ways can 6 people be divided into 2 groups of 3?
20
30
10
15
Questions & Step-by-Step Solutions
In how many ways can 6 people be divided into 2 groups of 3?
Correct Answer: 20
Step 1: Understand that we have 6 people and we want to divide them into 2 groups of 3.
Step 2: Calculate the total number of ways to arrange 6 people, which is 6! (6 factorial). This means 6 x 5 x 4 x 3 x 2 x 1 = 720.
Step 3: Since we are dividing them into 2 groups of 3, we need to account for the fact that the order of the groups does not matter. Therefore, we divide by the number of ways to arrange the 3 people in each group, which is 3! for the first group and 3! for the second group. So we calculate 3! = 3 x 2 x 1 = 6.
Step 4: We also need to divide by 2! (2 factorial) because the two groups themselves can be arranged in 2 different ways (Group A and Group B or Group B and Group A). 2! = 2 x 1 = 2.
Step 5: Now we can put it all together: The total number of ways to divide the 6 people into 2 groups of 3 is 6! / (3! * 3! * 2!) = 720 / (6 * 6 * 2) = 720 / 72 = 10.
Step 6: Therefore, the final answer is 10.
Combinatorics – The study of counting, arrangements, and combinations of objects.
Factorials – A mathematical operation that multiplies a number by all positive integers less than it.
Group Division – The process of splitting a set of items into distinct groups.
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