How many ways can 2 boys and 3 girls be selected from 5 boys and 6 girls?

How many ways can 2 boys and 3 girls be selected from 5 boys and 6 girls?

Step 1: Understand that we need to select 2 boys from a group of 5 boys.
Step 2: Use the combination formula to find the number of ways to choose 2 boys from 5. This is written as 5C2.
Step 3: Calculate 5C2. 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 4: For 5C2, calculate it as 5! / (2!(5-2)!) = 5! / (2! * 3!) = (5*4)/(2*1) = 10.
Step 5: Now, understand that we also need to select 3 girls from a group of 6 girls.
Step 6: Use the combination formula to find the number of ways to choose 3 girls from 6. This is written as 6C3.
Step 7: Calculate 6C3 using the same combination formula: 6C3 = 6! / (3!(6-3)!) = 6! / (3! * 3!) = (6*5*4)/(3*2*1) = 20.
Step 8: Now, multiply the number of ways to choose the boys and the girls together: 5C2 * 6C3 = 10 * 20.
Step 9: Calculate the final result: 10 * 20 = 200.
Step 10: Conclude that there are 200 ways to select 2 boys and 3 girls from the groups.

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