It Rearranges Itself!

Which of the following statements is true?

There are 3 ways to rearrange the letters in the word "THREE" There are 4 ways to rearrange the letters in the word "FOUR" There are 5 ways to rearrange the letters in the word "FIVE" There are 6 ways to rearrange the letters in the word "SIX"

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2 solutions

Zee Ell
Aug 20, 2016

Relevant wiki: Permutations without Repetition - Basic

There are 3! = 6 ways to rearrange the 3 letters of the word "six".

(While there are 4! = 24 ways to rearrange the 4 letters of the words "four" and "five" and 5! ÷ 2! = 60 ways to rearrange the 5 letters (of which the 2 "e"s are identical) of the word "three".)

Munem Shahriar
Jan 25, 2018

Statement: There are 3 ways to rearrange the word THREE.

Reply: Fasle \color{#D61F06} \boxed{\text{Fasle}} . It should be 5 ! 2 ! = 60 \dfrac{5!}{2! } = 60 ways.


Statement: There are 4 ways to rearrange the word FOUR.

Reply: Fasle \color{#D61F06} \boxed{\text{Fasle}} . It should be 4 ! = 24 4! = 24 ways.


Statement: There are 5 ways to rearrange the word FIVE.

Reply: Fasle \color{#D61F06} \boxed{\text{Fasle}} . It should be 4 ! = 24 4! = 24 ways.


Statement: There are 6 ways to rearrange the word SIX.

Reply: True \color{#20A900} \boxed{\text{True}} . There are 3 ! = 6 3! =6 ways.

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