A probability problem by Digi Verse

Probability Level 2

The word MATH and all the possible ways to rearrange the letters are written in alphabetical order. What number will MATH appear as? For example, AHMT would appear first, then AHTM next, etc.


The answer is 14.

Digi Verse by Digi Verse , 51, USA

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2 solutions

Brock Brown
Dec 26, 2014

The sequence of all 24 possible arrangements in alphabetical order is as follows:

1 AHMT

2 AHTM

3 AMHT

4 AMTH

5 ATHM

6 ATMH

7 HAMT

8 HATM

9 HMAT

10 HMTA

11 HTAM

12 HTMA

13 MAHT

14 MATH

15 MHAT

16 MHTA

17 MTAH

18 MTHA

19 TAHM

20 TAMH

21 THAM

22 THMA

23 TMAH

24 TMHA

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Digi Verse
Dec 26, 2014

All the entries beginning with A will come first, and there are 3! (6) of those, as will the words with H at the beginning, which there are 3! (6) of. Then M is next, though MAHT comes before MATH. therefore, 13 words come before MATH, and MATH would be the 14th one.

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