How do you figure this problem out?
How many different committees can be formed from 5 professors and 15 students if each committee is made up of 2 professors and 10 students?
THANKS!!!!!
The limiting factor is the students. You only have enough for one committee.
There are 5C2 ways to choose professors and 15C10 ways to select the students. Multiply them to get the total ways this can be done.
nCm means n choose m,check your text on how to calculate this.
There are 10 professors and 20 students out of whom a committee of 2 professors and 3 students is to be formed .find the number of ways in which tish can be done . further in how many of these committees
To calculate the number of ways to choose professors and students for the committee, we need to use the concept of combinations, also known as "n choose m" or written as nCm. We use this formula to calculate the possible combinations of selecting m items from a group of n items.
In this case, we need to calculate the combination of 5 professors taken 2 at a time (2 professors in a committee) and the combination of 15 students taken 10 at a time (10 students in the committee).
The formula for calculating combinations is given by:
nCm = n! / (m! * (n-m)!)
where "!" denotes the factorial of a number.
Let's calculate each combination separately and then multiply them to get the total number of different committees that can be formed.
For professors:
5C2 = 5! / (2! * (5-2)!)
= 5! / (2! * 3!)
= (5 * 4 * 3!) / (2! * 3!)
= (5 * 4) / 2!
= (5 * 4) / (2 * 1)
= 10
There are 10 different ways to select 2 professors from a group of 5.
For students:
15C10 = 15! / (10! * (15-10)!)
= 15! / (10! * 5!)
= (15 * 14 * 13 * 12 * 11 * 10!) / (10! * 5!)
= (15 * 14 * 13 * 12 * 11) / (5 * 4 * 3 * 2 * 1)
= 30,030
There are 30,030 different ways to select 10 students from a group of 15.
To find the total number of different committees that can be formed, we multiply the two combinations together:
Total number of committees = 10 * 30,030
= 300,300
Therefore, there are 300,300 different committees that can be formed from the given group of 5 professors and 15 students, with each committee consisting of 2 professors and 10 students.
5 taken 2=10
15 taken 10= [15x14x13x12x11]/5!
so the final answer is: [15x14x13x12x11x10]/5!