Arrangements

Probability Level 1

Rearranging all of the letters of the word MATHEMATICS, how many distinct strings can we form?


The answer is 4989600.

Paola Ramírez by Paola Ramírez , 24, Mexico

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4 solutions

Ralph James
Apr 29, 2016

There are 11 ! 11! different ways to arrange the letters. However, to account for distinctiveness, we have to account for letters that occur greater than one ( M , A , T M, A, T all occur twice in the word).

⟹ 11 ! 2 ! 2 ! 2 ! = 39916800 8 = 4989600 \implies \dfrac{11!}{2!2!2!} = \dfrac{39916800}{8} = \boxed{4989600}

26 Helpful 0 Interesting 3 Brilliant 2 Confused

I don't think that matters, you will still use those repeated letters in your new arrangements, so it should just be 11!

John Kamin - 4 years, 5 months ago

isn't it 6652800??or am i wrong haha

Yvonne Steele - 3 years, 8 months ago

For those who are a little confused, there are also 8 1! in the denominator product, but since they don't contribute, they have been not explicitly shown.

Mariusz Popieluch - 1 year, 4 months ago
Md Sadman Mufrad
Sep 26, 2020

BE PATIENT TO UNDERSTAND, OTHERWISE SKIP IT

  • What if it would be the word ' Mathematics ' to rearrange ( CAUTION: not only arrange ) all of the letters in all possible distinct strings?
  • Aren't the 'M' & 'm' same to be counted?
  • No, their face is totally different.
  • But bro, I found no difference between them, as they are the same letter.
  • Though they are of the same vocal, the permutation is NOT about the vocal, it is about the arrangement.
  • M is m, whatever you care.
  • Be patient, 'M' is not identical to 'm'. As we need to form possible strings, not merely a word of letters.
  • To arrange all of the letters, you must take M = m since the arrangement of letters is wanted. Aren't 'M' & 'm' the same letter?
  • ...
  • ....
  • .....
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What did you think about this problem? Please write down below, if you are engaged in it.

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1 Helpful 0 Interesting 0 Brilliant 0 Confused

11!/2!2!2!= 4989600

2 Helpful 0 Interesting 0 Brilliant 1 Confused
Diego Aguirre
Aug 3, 2017

M A and T are repeated

0 Helpful 0 Interesting 0 Brilliant 1 Confused

There are 11! in total in the word MATHEMATICS and the word has three repeating words 'M', 'A' and 'T'. So, we have to remove the repeating words for the possible outcomes. So, we have to divide 11! by 2! * 2! * 2!. It will result in 39916800 / 2 * 2 * 2 . So, our final answer would be 4989600.

Parthiban JP - 2 years ago

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