Which should be used a permutation or combination?

Determine the number of different ways in which a committee of four can be chosen from a group of twelve members?

please check my answer = combination

yes, combination is correct.

Now, how many such committees are there ?

To determine whether to use a permutation or combination, we need to consider two factors: order and repetition.

Permutation:
- Order matters. The arrangement of the elements is important.
- Each element can only be selected once.

Combination:
- Order does not matter. The arrangement of the elements is not important.
- Each element can only be selected once.

In the given question, we need to determine the number of different ways in which a committee of four can be chosen from a group of twelve members.

Since the order of the committee members does not matter (it's not important who is selected first, second, third, or fourth) and each member can be selected only once, we need to use combinations.

To calculate combinations, we can use the formula:
C(n, r) = n! / (r! * (n-r)!)

Where:
C(n, r) represents the number of combinations.
n represents the total number of elements.
r represents the number of elements to be chosen.

In this case, n = 12 (total number of members) and r = 4 (number of members to be chosen).

Thus, we can use the combination formula to find the number of different ways to choose a committee of four from twelve members:
C(12, 4) = 12! / (4! * (12-4)!)

Evaluating the expression:
C(12, 4) = 12! / (4! * 8!)

Calculating the factorials:
12! = 12 * 11 * 10 * 9 * 8!
4! = 4 * 3 * 2 * 1

Substituting the values:
C(12, 4) = (12 * 11 * 10 * 9 * 8!) / (4 * 3 * 2 * 1 * 8!)

Simplifying the expression:
C(12, 4) = (12 * 11 * 10 * 9) / (4 * 3 * 2 * 1) = 495

Therefore, the number of different ways in which a committee of four can be chosen from a group of twelve members is 495.