Question

Question 3 (20 points) (a) How many words with or without meaning, can be formed by using all the letters of the word, 'INSAN- ITY' using each letter exactly once? (b) How many words with or without meaning, can be formed by using all the letters of the word, 'TENNESSEE' using each letter exactly once?

Answer 1

Answer:

a)

Given,

Word INSANITY

Here the word INSANITY has 8 letters with 2 I's , 2 N's & remaining were different

So,

Number of arrangements = 8! / (2!*2!*1!*1!*1!*1!)

= 8! / (2*2)

= (8*7*6*5*4*3*2*1) / 4

= 10080

b)

Given word TENNESSEE

Here the word contains 9 letters with 4 E's , 2 N's , 2 S's & 1 T

So, they can arrange in = 9! / (4!*2!*2!*1!)

= (9*8*7*6*5*4*3*2*1) / (4*3*2*1*2*2*1)

= 3780