Question

how many 5-letter combinations can be created from the letters in the word \friendly\? assume that the order of the letters does not matter.
56
120
6,720
40,320

Explanation:

Step1: Count total unique letters

The word "friendly" has 8 unique letters: f, r, i, e, n, d, l, y. So $n=8$.

Step2: Define combination parameters

We choose 5 letters, so $k=5$. Use combination formula:
$$C(n,k)=\frac{n!}{k!(n-k)!}$$

Step3: Substitute values into formula

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

Step4: Simplify the factorial expression

$$\frac{8\times7\times6\times5!}{5!\times3\times2\times1}=\frac{8\times7\times6}{6}=56$$

Answer:

A. 56