Problem: A student has ten posters to pin up on the walls of her room, but there is space for only
seven. In how many ways can she choose the posters to be pinned up?
Solution: Identify whether it is permutation or combination. Then, give what is ask and select
which formula to be used. Substitute the given values.
Permutation
Combination
n = ______
n = ______
r = ______
r = ______
To solve this problem, we need to determine if it requires permutation or combination.
Permutation is used when the order of the items matters, while combination is used when the order does not matter.
In this case, the order in which the posters are chosen does not affect the outcome, as long as the seven selected posters are pinned up. Therefore, we need to use the combination formula.
Now, let's substitute the given values into the combination formula.
n represents the total number of posters available, which is 10.
r represents the number of posters to be pinned up, which is 7.
Using the combination formula, it is represented as:
C(n, r) = n! / (r!(n - r)!)
Substituting the values into the formula:
C(10, 7) = 10! / (7!(10 - 7)!)
Simplifying:
C(10, 7) = 10! / (7! * 3!)
Now, let's calculate the factorials:
10! = 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1
7! = 7 * 6 * 5 * 4 * 3 * 2 * 1
3! = 3 * 2 * 1
Calculating the combinations:
C(10, 7) = (10 * 9 * 8 * 7!) / (7! * 3!)
C(10, 7) = (10 * 9 * 8) / (3 * 2 * 1)
C(10, 7) = 720 / 6
C(10, 7) = 120
Therefore, there are 120 ways in which the student can choose the posters to be pinned up on the walls of her room.