Question

how many five - letter permutations can be formed from the first eight letters of the alphabet?

Explanation:

Step1: Identify permutation formula

We use the permutation formula \(P(n,k)=\frac{n!}{(n-k)!}\), where \(n=8\) (total letters), \(k=5\) (letters per permutation).

Step2: Substitute values into formula

$$P(8,5)=\frac{8!}{(8-5)!}=\frac{8!}{3!}$$

Step3: Expand factorials and simplify

$$\frac{8\times7\times6\times5\times4\times3!}{3!}=8\times7\times6\times5\times4$$

Step4: Calculate the product

$$8\times7=56;\ 56\times6=336;\ 336\times5=1680;\ 1680\times4=6720$$

Answer:

6720 permutations