Question

Number of words that can be formed from the letters of the word ENGINEER so that order of vowels do not change is

• A. 48
• B. 144
• C. 216
• D. 840

Answer 1

Answer: (D)

840

Answer 2

Here vowels are in the order E, I, E, E. Order of the vowels does not change means in the arrangement when ever we look order of vowel in EIEE (for example NGEINEER is accepted but NGIENEER is not accepted as vowels are in order IEEE).

Suppose I is replaced by E (i.e, all the vowels are considered to be identical) now order of vowels are always same whatever arrangement is made and this is the required number of ways we are looking for

∴ Required ways = $\frac{8!}{4!\mspace{6mu} 2!}$ = 840.