How many ways can 2 boys and 3 girls be selected from a group of 5 boys and 7 gi

How many ways can 2 boys and 3 girls be selected from a group of 5 boys and 7 girls? (2018)

How many ways can 2 boys and 3 girls be selected from a group of 5 boys and 7 girls? (2018)

Step 1: Identify the total number of boys and girls. We have 5 boys and 7 girls.
Step 2: Determine how many boys we need to select. We need to select 2 boys.
Step 3: Use the combination formula to find the number of ways to select 2 boys from 5. This is calculated as 5C2.
Step 4: Calculate 5C2. The formula for combinations is nCr = n! / (r!(n-r)!). So, 5C2 = 5! / (2!(5-2)!) = 10.
Step 5: Now, determine how many girls we need to select. We need to select 3 girls.
Step 6: Use the combination formula to find the number of ways to select 3 girls from 7. This is calculated as 7C3.
Step 7: Calculate 7C3. Using the combination formula, 7C3 = 7! / (3!(7-3)!) = 35.
Step 8: Multiply the number of ways to select boys and girls together. Total ways = 5C2 * 7C3 = 10 * 35.
Step 9: Calculate the total. 10 * 35 = 350.

Combinatorics – The question tests the understanding of combinations, specifically how to choose a subset of items from a larger set without regard to the order of selection.
Binomial Coefficients – The use of binomial coefficients (nCr) to calculate the number of ways to choose r items from n items is a key concept in solving this problem.