Question

How many permutations can be formed from all the letters in the word a) 39,916,800 b) 435,600 c) 277,200 d) 144 e) 108,900 f) None of the above. ENGINEERING?

Answer 1

Answer: c) 277,200

Step-by-step explanation:

The number of permutations can be formed of n things , where a things are like b things are like and so on :

$\dfrac{n!}{a!\ b!....}$

The given word : ENGINEERING

Total letters = 11

Number of E's = 3

Number of N's = 3

Number of G's =2

Number of I's =2

The number of permutations can be formed from all the letters in the word "ENGINEERING" will be :

$\dfrac{11!}{3!3!2!2!}\\\\=\dfrac{11\times10\times9\times8\times7\times6}{6\times6\times2\times2}\\\\=277200$

Hence, the number of permutations can be formed from all the letters in the word "ENGINEERING" = 277,200

∴ Correct answer is c) 277,200