Question

all the arrangements, with or without meaning, of the word farmer are written excluding any word that has two r appearing together. the arrangements are listed serially in the alphabetic order as in the english dictionary. then the serial number of the word farmer in this list is .

Answer 1

The serial number is found by adding 1 to this tally, considering the specific rules about the letter 'r'. The word "farmer" is at position 7.

Step-by-step explanation:

To determine the serial position of the word "farmer" when arranging its letters alphabetically, while excluding instances where two consecutive 'r's appear, a systematic approach is taken. Starting with combinations beginning with 'a-', the first valid permutation is 'aefmrr'. However, as double 'r' occurrences are to be avoided, we progress to the next set starting with 'f-', then 'fa-', 'far-', 'farm-', until reaching 'farmer'.

It becomes evident that 'farmer' is the earliest valid permutation after considering all 'fa-' starting arrangements without consecutive 'r's. To find its position, we calculate the number of valid permutations before 'farmer' and add 1. Notably, accounting for the duplicated 'r', the permutations of 'farmer' are 5! (factorial of 5), but halved due to the repeated 'r'. In this ordered list, "farmer" occupies the seventh position.