How many different ways are there for an admissions officer to select a group of 7 college candidates from a group of 19 applicants for an interview?
Since the order in which they are picked does not matter, the number of combinations is 19!/(7!*12!)=
19*18*17*16*15*14*13/(2*3*4*5*6*7) =?
(Do the numbers or use a hand calculator. Many have keys for the factorial (!) function.)
To find the number of different ways to select a group of 7 college candidates from a group of 19 applicants for an interview, you 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 applicants and r is the number of candidates to be selected.
In this case, we have n = 19 (total applicants) and r = 7 (candidates to be selected).
Using the formula, we can calculate the number of combinations as follows:
C(19, 7) = 19! / (7!(19 - 7)!)
C(19, 7) = 19! / (7!12!)
Now, let's simplify this expression:
19! = 19 * 18 * 17 * 16 * 15 * 14 * 13 * 12!
7! = 7 * 6 * 5 * 4 * 3 * 2 * 1
12! = 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1
Substituting these values into the formula:
C(19, 7) = (19 * 18 * 17 * 16 * 15 * 14 * 13 * 12!) / (7 * 6 * 5 * 4 * 3 * 2 * 1 * 12!)
Now, we can cancel out the common terms:
C(19, 7) = (19 * 18 * 17 * 16 * 15 * 14 * 13) / (7 * 6 * 5 * 4 * 3 * 2 * 1)
At this point, you can either calculate the expression manually or use a calculator that has a factorial (!) function.
Calculating this expression will give you the number of different ways an admissions officer can select a group of 7 college candidates from a group of 19 applicants for an interview.