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.