Question

Use the permutation formula to solve a problem when

n=8 and r=4.
a) 420
b) 1,680
c) 6,720
d) 26,880

Answer 1

The permutation formula for n=8 and r=4 yields
`\(P^8_4 = 8 * 7 * 6 * 5 = 1,680\)`, thus the correct option is b.

Step-by-step explanation:

Permutation is a mathematical concept used to count the number of ways to arrange objects in a specific order. The permutation formula is expressed as
`\(P^n_r = (n!)/((n-r)!)\)`, where n is the total number of objects and r is the number of objects taken at a time. For this problem with n=8 and r=4, we substitute these values into the formula.

The permutation formula
`\(P^8_4 = (8!)/((8-4)!)\)` represents selecting 4 objects out of 8 and arranging them in a specific order. Calculating 8! (8 factorial) gives
`\(8 * 7 * 6 * 5 = 1,680\)`. The denominator 8-4)! simplifies to 4!, which is
`\(4 * 3 * 2 * 1 = 24\)`. Dividing 8! by 4! results in 1,680, which represents the number of permutations for arranging 4 objects out of 8 in a specific order.

Therefore, using the permutation formula, the result for n=8 and r= is
`\(P^8_4 = 1,680\)`. This calculation illustrates the number of ways we can arrange 4 objects out of a total of 8 in a particular sequence, emphasizing the significance of order in the arrangement process. Hence, option b) 1,680 is the correct answer based on the permutation formula calculation for these values of n and r.