A school district has 2 teaching positions to fill and there are 8 applicants to choose from. How many
different possibilities are there?
28
To find the number of different possibilities, we need to calculate the combination (nCr) of selecting 2 applicants out of 8. The formula for combination is:
nCr = n! / (r! * (n-r)!)
where n is the total number of applicants and r is the number of positions to fill.
In this case, n = 8 and r = 2. Plugging these values into the formula, we get:
8C2 = 8! / (2! * (8-2)!)
= 8! / (2! * 6!)
= (8 * 7 * 6!) / (2! * 6!)
= (8 * 7) / 2!
= 56 / 2
= 28.
Therefore, there are 28 different possibilities to fill the 2 teaching positions from 8 applicants in the school district.
To find the number of different possibilities, you need to calculate the number of combinations. In this case, we want to choose 2 applicants from a pool of 8. You can use the formula for combinations:
C(n, r) = n! / (r!(n-r)!)
Where n is the total number of options (applicants) and r is the number of options to choose (teaching positions).
Applying the formula:
C(8, 2) = 8! / (2!(8-2)!)
= 8! / (2!6!)
= (8 * 7 * 6!) / (2! * 6!)
= (8 * 7) / 2!
= 56 / 2
= 28
Therefore, there are 28 different possibilities to choose 2 applicants from a pool of 8 for the 2 teaching positions.
A school district has 2 teaching positions to fill and there are 8 applicants to choose from. How many
different possibilities are there?
A. 28
B. 3
C. 56
D. 4 My answer