Compute:

The number of combinations of 8 elements taken 3 at a time.

The number of permutations of 8 elements taken 3 at at time.

To compute the number of combinations and permutations, we can use the formulas:

1. The number of combinations, denoted as C(n, r), is given by the formula:
C(n, r) = n! / (r! * (n-r)!)

2. The number of permutations, denoted as P(n, r), is given by the formula:
P(n, r) = n! / (n-r)!

Now, let's calculate the number of combinations and permutations for your specific case:

1. Number of combinations of 8 elements taken 3 at a time:
C(8, 3) = 8! / (3! * (8-3)!)
= 8! / (3! * 5!)
= (8 * 7 * 6) / (3 * 2 * 1)
= 56

Therefore, the number of combinations of 8 elements taken 3 at a time is 56.

2. Number of permutations of 8 elements taken 3 at a time:
P(8, 3) = 8! / (8-3)!
= 8! / 5!
= (8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / (5 * 4 * 3 * 2 * 1)
= (8 * 7 * 6)
= 336

Therefore, the number of permutations of 8 elements taken 3 at a time is 336.

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