Question

The letters in the word ROADIE are permuted in all possible ways and arranged in alphabetical order. Find the word in the 44th rank?
a) AERIOD
b) AERDOI
c) AERODI
d) AEODRI

Answer 1

very interesting question,
given word is ROADIE
number of words form when first letter is A = 5!
= 5 × 4 × 3 × 2 × 1 = 120
number of words form when first two letters is AD = (6 - 2)! = 4! = 24
number of words form when first three latters is AED = (6 - 3)! = 3! = 6
number of words form when first three latters is AEI = (6 - 3)! = 3! = 6

Let's check how much words are formed = 24 + 6 + 6 = 42
hence, 42th word is AEIDOR
43th word is AERDIO
44th word is AERDOI

hence, option (b) is correct.

Answer 2

Answer:

Step-by-step explanation:

number of words form when first letter is A = 5!

= 5 × 4 × 3 × 2 × 1 = 120

number of words form when first two letters is AD = (6 - 2)! = 4! = 24

number of words form when first three latters is AED = (6 - 3)! = 3! = 6

number of words form when first three latters is AEI = (6 - 3)! = 3! = 6

Let's check how much words are formed = 24 + 6 + 6 = 42

hence, 42th word is AEIDOR

43th word is AERDIO

44th word is AERDOI