A student dance committee is to be formed consisting of 3 boys and 4 girls. If the membership is to be chosen from 7 boys and 6 girls, how many different committees are possible?
525
To determine the number of different committees that can be formed, we need to use the concept of combinations.
The number of ways to choose a committee of 3 boys from a group of 7 can be calculated as "7 choose 3", which is denoted as C(7,3) or written as 7C3. This can be calculated as:
C(7,3) = 7! / (3! * (7 - 3)!) = (7 * 6 * 5) / (3 * 2 * 1) = 35
Similarly, the number of ways to choose a committee of 4 girls from a group of 6 is "6 choose 4", denoted as C(6,4) or written as 6C4. This can be calculated as:
C(6,4) = 6! / (4! * (6 - 4)!) = (6 * 5) / (2 * 1) = 15
To find the total number of different committees possible, we need to multiply the number of ways to choose the boys and the girls together since they are independent events.
Total number of different committees = C(7,3) * C(6,4)
= 35 * 15
= 525
Therefore, there are 525 different committees possible.
To determine the number of different committees that are possible, we can use the concept of combinations.
First, let's determine the number of ways we can select 3 boys from a group of 7. This can be calculated using the combination formula, given by:
C(n, r) = n! / (r!(n - r)!),
where C(n, r) represents the number of ways to choose r items from a set of n items, and n! denotes the factorial of n.
Using this formula, we can calculate the number of ways to select 3 boys from 7:
C(7, 3) = 7! / (3!(7 - 3)!) = (7 * 6 * 5) / (3 * 2 * 1) = 35.
Now, let's determine the number of ways we can select 4 girls from a group of 6:
C(6, 4) = 6! / (4!(6 - 4)!) = (6 * 5) / (2 * 1) = 15.
Since we need to select both the boys and the girls, we can multiply these two numbers together to get the total number of different committees possible:
35 * 15 = 525.
Therefore, there are 525 different committees possible.