How many ways can 2 men and 3 women be selected from a group of 5 men and 6 women? (2020)
Practice Questions
1 question
Q1
How many ways can 2 men and 3 women be selected from a group of 5 men and 6 women? (2020)
100
60
120
80
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.
Questions & Step-by-step Solutions
1 item
Q
Q: How many ways can 2 men and 3 women be selected from a group of 5 men and 6 women? (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.
Steps: 8
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.
