there are 15 boys and 10 girls in your class. a faur member committee is to befromedfrom the student of your class. in how many ways this can be done if the comittee consists at least three girls
with 3 girls:
= C(10,3) x C(15,1) = ..
with 4 girls
= C(10,4) x C(15,0) =
add them up
To find the number of ways to form a committee with at least three girls, we need to consider two cases: one where exactly three girls are selected and another where all four members are girls.
Case 1: Selecting exactly three girls:
To form a committee with exactly three girls, we need to select 3 girls from the 10 available girls and 1 boy from the 15 available boys.
The number of ways to choose 3 girls from a group of 10 is denoted as "10 choose 3," which can be calculated using the binomial coefficient formula.
10 choose 3 = 10! / (3! * (10 - 3)!) = 10! / (3! * 7!) = (10 * 9 * 8) / (3 * 2 * 1) = 120
Once the three girls are selected, we need to choose one boy from the remaining 15 boys. So, there are 15 ways to select the remaining boy.
Therefore, for Case 1, the total number of ways to form the committee is 120 * 15 = 1800.
Case 2: Selecting all four girls:
To form a committee with all four girls, we need to select all four girls from the 10 available girls.
The number of ways to choose 4 girls from a group of 10 is denoted as "10 choose 4."
10 choose 4 = 10! / (4! * (10 - 4)!) = 210
Therefore, for Case 2, the total number of ways to form the committee is 210.
To get the final answer, we need to add the results from both cases since we are considering either at least three girls or all four girls.
Final Answer: 1800 + 210 = 2010
Hence, there are 2010 ways to form the committee if it consists of at least three girls.