How many different combinations of four letters can be made from the word: MATHEMATICS?

Question

Not all the letters in the combinations have to be different.
The same combination of letters but using the different letters in a pair in the same space does not count.
E.g. MATH and MATH only count as one even though there are 2 Ms.
Remember, only combinations of 4 letters count.

Answer 1

You are looking, I assume, for ordered combinations (i.e. permutations).

Removing the duplicate M, A and T, we have 8 different letters from which we can make 8P4 = 8!/4! = 1680 permutations.

We need to add words having two M's and two other distinct letters: Pick two spots for the M's (4C2 ways) and then assign the 7 other letters the two other spots (7P2). So we have (4C2)*(7P2) = 6 * 42 = 252 more possibilities.

We do the same for words with two A's and those with two T's, so we're now at 1680 + 3*252 = 2436.

We also need to add words having pairs of identical letters like MAMA and TAAT... For two M's and two A's, there are 4C2=6 possibilities. Same for M's and T's, and same for A's and T's. This add 18 to our total.

Answer: 2454, without regard to the restrictions of the English language.

Looking for English words: math mate mats mace mama mast mice mite mist mits mime meat came cats cams cast case cite sect site scat seat sate stem teas east ices aces acts that shat sh*t tact test aims maim tics t*ts them hams hems heat hats hate sham chat ...

Answer 2

Mathematically, as many people have proven, the maximum amount could be up to 4989600. But we know that’s impossible so here are the ones I’ve found. Okay here goes:
Math, Mate, Matt, Mats, Mace, Mast, Mash, Mass, Meat, Mete, Meme, Mesh, Mica, Mice, Mime, Mist, Mite, Mitt, Amah, Ails, Aim, Aits, Aces, Ache, Acts, Asci, Teas, Tame, Tash, Tats, That, Them, This, Heam, Hams, Hash, Hast, Hats, Hate, Hath, Heat, Hems, Hest, Hies, Hist, Hits, Emit, Each, East, Eats, Etch, Ices, Imam, Itch, Item, Came, Cast, Cats, Case, Cash, Cite, Chai, Cham, Chat, Sect, Site, Scat, Tics, Ties, Time, T*ts, Cain, Sate, Sati, Scam, Seam, Seat, Sets, Sett, Sham, Shat, Shea, Shim, Sh*t (its in the OED), Stem, Sice, Site, Test, Tact, Same, Stet.

Some Informal words that could be included are Stat, Semi, Meth, Mama, and Mams. Some proper nouns include Shia, Thai and Cams. Eta, Eth and Chi are all letters of an alphabet (first two Greek, last one Chinese), and if you were to pluralize them by adding an s they would be a further three. However I’m not sure to their plurals, as I’m also not with Ahi, but that could be another one with an s on the end. Admittedly 'Hast', 'Hath', 'Hest' and 'Hies' are all archaic so they could be omitted. In all, if you count the ones I’m not sure of it makes 104 words, and I’ve probably missed a few.

Answer 3

I got this far and then gave up - expect there are far more

Math Mate Mats Meat Mame Mime Mite Mist Mash MastTime Tame Team Them That This Tics Ties Hate Heat Hats Aims Atic Eats East Seat Same Stem Seam Cash Cats Chat Came

33 not bad although expect others can do better lol!

Answer 4

If each of the letters were different it must be 11 factorial, i.e. 11x10x9x8x7x6x5x4x3x2x1 = 39,916,800. yet you've 3 gadgets of two letters (2 As, 2Ts, 2Ms). the reply is subsequently decreased by using a ingredient of 2x2x2, or a ingredient of 8. Divide the above by using 8. very last answer is 4,989,600.

Answer 5

11!/2!2!2!

= 39916800/8

= 4989600 different combinations

[note: x! is mathematical notation for x*(x-1)*(x-2)*...*3*2*1]

Answer 6

11!/2!2!2!

= 4989600 WORDS U CAN MAKE FROM MATHEMATICS

Answer 7

them

Answer 8

math
matt
them
scam
that
tame
mate
emma

Answer 9

hate
mate
time
mime
mame
tame
came
same
them
that
this
hats
mats
sh*t