A 10 person student council will be selected from 18 students at a school. How many poss are there for this council?
combinations of 18 taken 10 at a time
= 18!/[ 10!(18-10)!]
= 18*17*16*15*14*13*12*11/
(8*7*6*5*4*3*2)
= 17*16*15*14*13*12*11/(8*7*5*4*2)
= 17*15*14*13*12*11/(7*5*4)
= 17*3*2*13*3*11
= 43,758
To find the number of possible student council combinations, we can use the combination formula.
The formula for combinations is given by:
C(n, r) = n! / (r!(n-r)!),
where n is the total number of students, and r is the number of students to be selected for the council.
In this case, n = 18 (total students) and r = 10 (students on the council).
Therefore, the number of possible combinations for the student council is:
C(18, 10) = 18! / (10!(18-10)!) = 18! / (10! * 8!)
Please note that "!" denotes the factorial of a number.
Calculating the factorials:
18! = 18 * 17 * 16 * 15 * 14 * 13 * 12 * 11 * 10!
10! = 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1
8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1
Substituting the values into the combination formula:
C(18, 10) = (18 * 17 * 16 * 15 * 14 * 13 * 12 * 11 * 10!) / (10! * (8 * 7 * 6 * 5 * 4 * 3 * 2 * 1))
Simplifying the expression:
C(18, 10) = (18 * 17 * 16 * 15 * 14 * 13 * 12 * 11) / (8 * 7 * 6 * 5 * 4 * 3 * 2 * 1)
Calculating the multiplication of the numerator:
18 * 17 * 16 * 15 * 14 * 13 * 12 * 11 = 18,336,422,400
Calculating the multiplication of the denominator:
8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 40,320
Finally, dividing the numerator by the denominator:
C(18, 10) = 18,336,422,400 / 40,320 = 456,789,600
Therefore, there are 456,789,600 possible combinations for the student council from 18 students.
To find the number of possible ways to select a 10 person student council from 18 students, we can use the concept of combinations. The formula for combinations is given by:
C(n, k) = n! / (k! * (n-k)!)
Where n is the total number of students (18) and k is the number of students to be selected (10). The exclamation mark "!" denotes factorial, which means multiplying a number by all the positive integers less than itself down to 1.
Now let's substitute the values into the formula and calculate:
C(18, 10) = 18! / (10! * (18-10)!)
= 18! / (10! * 8!)
To simplify the calculation, we can cancel out common terms between the numerator and denominator. In this case, we can cancel out the factorials of 10, 9, 8, 7, 6, 5, 4, 3, 2, and 1.
C(18, 10) = (18 * 17 * 16 * 15 * 14 * 13 * 12 * 11) / (10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1)
Now, we can perform the multiplication:
C(18, 10) = 243,928,800 / 3,628,800
Simplifying further:
C(18, 10) = 67,860
Therefore, there are 67,860 possible ways to select a 10 person student council from 18 students.