Question

Find the number of distinguishable permutations of the letters in the

given words.
a) spring
b) eagles

Answer 1

The number of distinguishable permutations for 'spring' is 720, and for 'eagles', taking into account the repeated 'e', is 360.

Step-by-step explanation:

To find the number of distinguishable permutations of the letters in the words 'spring' and 'eagles', we can use the formula for permutations of a set of objects where some of the objects are identical. The formula is:

1. 
   Calculate the factorial of the number of total elements (n!).
2. 
   For each set of identical elements, calculate the factorial of the number of those elements.
3. 
   Divide the factorial of the total number by the factorial of each set of identical elements.

For the word spring, since all letters are unique, we have 6 different letters. Thus, the number of permutations is 6! (six-factorial), which is 720.

For the word eagles, we have 6 letters with the letter 'e' repeating. So, the number of permutations is:

6! / 2! = (6*5*4*3*2*1)/(2*1) = 720 / 2 = 360

There are 720 distinguishable permutations of the letters in 'spring' and 360 distinguishable permutations of the letters in 'eagles'.