Final answer:
BEAN has a greater number of permutations than BEEN because BEAN has no repeating letters, leading to 24 permutations, while BEEN has repeating letters, resulting in only 12 permutations.
Step-by-step explanation:
The question involves determining which word, BEAN or BEEN, has the greater number of permutations of all its letters. A permutation is a way of rearranging the letters of a word or set to create different combinations.
To find the number of permutations of a word, we use the formula n! divided by the product of the factorials of the frequency of each letter in the word, where n is the total number of letters.
For BEAN, there are no repeating letters, so the number of permutations would be 4!, which is 4 x 3 x 2 x 1 = 24 permutations.
For BEEN, the letter E repeats twice. Thus, the number of permutations is 4! divided by 2!, which is (4 x 3 x 2 x 1)/(2 x 1) = 12 permutations.
Therefore, the word BEAN has a greater number of permutations than the word BEEN.