Question

The letters of the word BRONZE are written in all possible orders. How many words are possible? If these words are written out in a dictionary order, what is the rank of the word BRONZE?

Answer 1

Answer:

82

Step-by-step explanation:

Hi,

Given that the letters of the word BRONZE are written in all

possible orders.

Since there are 6 letters in the given word and the number of

ways in which 6 letters can be arranged among themselves

would be 6! = 720.

Letters of the word BRONZE in alphabetical order are B, E, O, N,

R, Z

So, if all the words are written in a dictionary order firstly

Words starting with BE : the last 4 can be permuted in 4! = 24

ways

Words starting with BO : Again last 4 can be permuted in 4! = 24

ways

Words starting with BN : Again last 4 can be permuted in 4! = 24

ways

Words starting with BRE the last 3 can be permuted in 3!  = 6

 ways

Words starting with BROE the last 2 can be permuted in 2!  = 2

ways

Words starting with BRONE there is only 1 word BRONEZ and

then next comes BRONZE.

So, the rank of word BRONZE is 3*24 + 6 + 2 + 1 + 1 = 82

Hence, BRONZE is 82 nd word .

Hope, it helps !