How many ways can 2 boys and 3 girls be selected from 8 boys and 6 girls?

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Q: How many ways can 2 boys and 3 girls be selected from 8 boys and 6 girls?

Solution: The number of ways is 8C2 * 6C3 = 28 * 20 = 560.

Steps: 6

Step 1: Understand the problem. We need to select 2 boys from a group of 8 boys and 3 girls from a group of 6 girls.
Step 2: Use the combination formula to find the number of ways to choose boys. The formula for combinations is nCr = n! / (r! * (n - r)!), where n is the total number of items, r is the number of items to choose, and '!' denotes factorial.
Step 3: Calculate the number of ways to choose 2 boys from 8 boys. This is 8C2 = 8! / (2! * (8 - 2)!) = 8! / (2! * 6!) = (8 * 7) / (2 * 1) = 28.
Step 4: Calculate the number of ways to choose 3 girls from 6 girls. This is 6C3 = 6! / (3! * (6 - 3)!) = 6! / (3! * 3!) = (6 * 5 * 4) / (3 * 2 * 1) = 20.
Step 5: Multiply the number of ways to choose boys and girls together. This gives us the total number of ways to select 2 boys and 3 girls: 28 * 20 = 560.
Step 6: Conclude that there are 560 different ways to select 2 boys and 3 girls from the given groups.