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

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Q: In how many ways can 2 boys and 3 girls be selected from 5 boys and 6 girls?

Solution: The number of ways is C(5,2) * C(6,3) = 10 * 20 = 200.

Steps: 6

Step 1: Understand that we need to select 2 boys from a group of 5 boys.
Step 2: Use the combination formula C(n, r) which means 'n choose r'. Here, n is the total number of items, and r is the number of items to choose.
Step 3: Calculate C(5, 2) which is the number of ways to choose 2 boys from 5. The formula is C(n, r) = n! / (r! * (n - r)!). So, C(5, 2) = 5! / (2! * (5 - 2)!) = 5! / (2! * 3!) = (5 * 4) / (2 * 1) = 10.
Step 4: Now, we need to select 3 girls from a group of 6 girls.
Step 5: Calculate C(6, 3) using the same combination formula. C(6, 3) = 6! / (3! * (6 - 3)!) = 6! / (3! * 3!) = (6 * 5 * 4) / (3 * 2 * 1) = 20.
Step 6: Multiply the number of ways to choose boys and girls together. So, the total number of ways = C(5, 2) * C(6, 3) = 10 * 20 = 200.