Question

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

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?

#### Homework Answers

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

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