Question

Find the number of distinguishable permutations of the letters in the given word.

Answer 1

Answer:

5 040 permutations

Step-by-step explanation:

the word ‘HONOLULU’ has 8 letters

In this word ,the letters O , L and U are repeated each two times.

the number of permutations of the two letters O , o is 2!

the number of permutations of the two letters L , L is 2!

the number of permutations of the two letters U , U is 2!

the number of permutations (distinguishable or not) of the letters in HONOLULU is 8!

then

the number of distinguishable permutations of the letters in HONOLULU :

$=\frac{8!}{2!\times 2!\times 2!}$

$=5040$