SOLUTION: How do you solve this question: How many permutations of the word MINIMUM begin with an "m"?

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Question 947200: How do you solve this question:
How many permutations of the word MINIMUM begin with an "m"?
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
MINIMUM

If we put M first, then we just have to find the distinguishable
arrangements of "INIMUM" to put after it:

"INIMUM" has 6 letters with two indistinguishable I's and two
indistinguishable M's. Therefore the number of distinguishable
arrangements of "INIMUM" is 6%21%2F%282%212%21%29+=+180 ways.

Answer: 180

As a computer check, here are all 180 distinguishabe arrangments
of "MINIMUM" in alphabetical order. Number 38 is "MINIMUM" itself!: 


  1.MIIMMNU   2.MIIMMUN   3.MIIMNMU   4.MIIMNUM   5.MIIMUMN   6.MIIMUNM   7.MIINMMU   8.MIINMUM   9.MIINUMM  10.MIIUMMN
 11.MIIUMNM  12.MIIUNMM  13.MIMIMNU  14.MIMIMUN  15.MIMINMU  16.MIMINUM  17.MIMIUMN  18.MIMIUNM  19.MIMMINU  20.MIMMIUN
 21.MIMMNIU  22.MIMMNUI  23.MIMMUIN  24.MIMMUNI  25.MIMNIMU  26.MIMNIUM  27.MIMNMIU  28.MIMNMUI  29.MIMNUIM  30.MIMNUMI
 31.MIMUIMN  32.MIMUINM  33.MIMUMIN  34.MIMUMNI  35.MIMUNIM  36.MIMUNMI  37.MINIMMU  38.MINIMUM  39.MINIUMM  40.MINMIMU
 41.MINMIUM  42.MINMMIU  43.MINMMUI  44.MINMUIM  45.MINMUMI  46.MINUIMM  47.MINUMIM  48.MINUMMI  49.MIUIMMN  50.MIUIMNM
 51.MIUINMM  52.MIUMIMN  53.MIUMINM  54.MIUMMIN  55.MIUMMNI  56.MIUMNIM  57.MIUMNMI  58.MIUNIMM  59.MIUNMIM  60.MIUNMMI
 61.MMIIMNU  62.MMIIMUN  63.MMIINMU  64.MMIINUM  65.MMIIUMN  66.MMIIUNM  67.MMIMINU  68.MMIMIUN  69.MMIMNIU  70.MMIMNUI
 71.MMIMUIN  72.MMIMUNI  73.MMINIMU  74.MMINIUM  75.MMINMIU  76.MMINMUI  77.MMINUIM  78.MMINUMI  79.MMIUIMN  80.MMIUINM
 81.MMIUMIN  82.MMIUMNI  83.MMIUNIM  84.MMIUNMI  85.MMMIINU  86.MMMIIUN  87.MMMINIU  88.MMMINUI  89.MMMIUIN  90.MMMIUNI
 91.MMMNIIU  92.MMMNIUI  93.MMMNUII  94.MMMUIIN  95.MMMUINI  96.MMMUNII  97.MMNIIMU  98.MMNIIUM  99.MMNIMIU 100.MMNIMUI
101.MMNIUIM 102.MMNIUMI 103.MMNMIIU 104.MMNMIUI 105.MMNMUII 106.MMNUIIM 107.MMNUIMI 108.MMNUMII 109.MMUIIMN 110.MMUIINM
111.MMUIMIN 112.MMUIMNI 113.MMUINIM 114.MMUINMI 115.MMUMIIN 116.MMUMINI 117.MMUMNII 118.MMUNIIM 119.MMUNIMI 120.MMUNMII
121.MNIIMMU 122.MNIIMUM 123.MNIIUMM 124.MNIMIMU 125.MNIMIUM 126.MNIMMIU 127.MNIMMUI 128.MNIMUIM 129.MNIMUMI 130.MNIUIMM
131.MNIUMIM 132.MNIUMMI 133.MNMIIMU 134.MNMIIUM 135.MNMIMIU 136.MNMIMUI 137.MNMIUIM 138.MNMIUMI 139.MNMMIIU 140.MNMMIUI
141.MNMMUII 142.MNMUIIM 143.MNMUIMI 144.MNMUMII 145.MNUIIMM 146.MNUIMIM 147.MNUIMMI 148.MNUMIIM 149.MNUMIMI 150.MNUMMII
151.MUIIMMN 152.MUIIMNM 153.MUIINMM 154.MUIMIMN 155.MUIMINM 156.MUIMMIN 157.MUIMMNI 158.MUIMNIM 159.MUIMNMI 160.MUINIMM
161.MUINMIM 162.MUINMMI 163.MUMIIMN 164.MUMIINM 165.MUMIMIN 166.MUMIMNI 167.MUMINIM 168.MUMINMI 169.MUMMIIN 170.MUMMINI
171.MUMMNII 172.MUMNIIM 173.MUMNIMI 174.MUMNMII 175.MUNIIMM 176.MUNIMIM 177.MUNIMMI 178.MUNMIIM 179.MUNMIMI 180.MUNMMII
 

Edwin