Question

a biologist is attempting to classify 54,000 species of insects by assigning 3 initials to each species. is it possible to classify all the species in this way? if not, how many initials should be used? select the correct choice below, and if necessary, fill in the answer box to complete your choice. a. no, it is not possible to classify all the species by assigning 3 initials to each species. the biologist should use at least initials instead. b. yes, it is possible to classify all the species by assigning 3 initials to each species.

Explanation:

Step1: Calculate number of combinations with 3 initials

Assume 26 letters in the alphabet. The number of combinations of 3 - initials is $26\times26\times26=26^{3}=17576$.

Step2: Compare with number of species

Since $17576<54000$, it is not possible to classify all species with 3 initials.

Step3: Find number of initials needed

Let $n$ be the number of initials. We need $26^{n}\geq54000$.
$26^{4}=26\times26\times26\times26 =456976\geq54000$. So at least 4 initials are needed.

Answer:

A. No, it is not possible to classify all the species by assigning 3 initials to each species. The biologist should use at least 4 initials instead.