Question

2. (a) In how many ways, can you arrange the letters in the word “Massachusetts”?

(b) Let’s introduce an additional constraint: a vowel letter has to be the first letter in your arrangement. How many ways can you arrange these letters now?

Answer 1

"Massachusetts" has

1 m, 2 a, 4 s, 1 c, 1 h, 1 u, 1 e, 2 t

Total of 13 letters

(a) The number of ways in which the letters in the word "Massachusetts" can be arranged

= 13!/(2!*4!*2!)

= 64,864,800

(b) There are a total of 4 vowels present in the given word

Number of ways to arrange the letters if the first letter is a

= 12!/(4!*2!)

Number of ways to arrange the letters if the first letter is u

= 12!/(2!*4!*2!)

Number of ways to arrange the letters if the first letter is e

= 12!/(2!*4!*2!)

Thus, total number of ways = 19,958,400