How many ways can 2 men and 3 women be selected from a group of 5 men and 6 wome

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Question: How many ways can 2 men and 3 women be selected from a group of 5 men and 6 women? (2020)

Options:

Correct Answer: 100

Exam Year: 2020

Solution:

The number of ways to select 2 men from 5 is 5C2 and 3 women from 6 is 6C3. Total = 5C2 * 6C3 = 10 * 20 = 200.

How many ways can 2 men and 3 women be selected from a group of 5 men and 6 women? (2020)

How many ways can 2 men and 3 women be selected from a group of 5 men and 6 women? (2020)

Step 1: Identify the total number of men and women available. We have 5 men and 6 women.
Step 2: Determine how many men we need to select. We need to select 2 men.
Step 3: Calculate the number of ways to select 2 men from 5. This is done using the combination formula, which is written as 5C2.
Step 4: Use the combination formula: 5C2 = 5! / (2! * (5-2)!) = 10. So, there are 10 ways to select 2 men.
Step 5: Now, determine how many women we need to select. We need to select 3 women.
Step 6: Calculate the number of ways to select 3 women from 6. This is done using the combination formula, which is written as 6C3.
Step 7: Use the combination formula: 6C3 = 6! / (3! * (6-3)!) = 20. So, there are 20 ways to select 3 women.
Step 8: Multiply the number of ways to select the men by the number of ways to select the women. This gives us the total number of ways to select 2 men and 3 women: 10 * 20 = 200.

Combinatorics – The question tests the understanding of combinations, specifically how to calculate the number of ways to choose a subset from a larger set.
Multiplication Principle – It assesses the application of the multiplication principle in counting, where the total number of combinations is the product of the combinations of each group.