A bag contains 26 tiles, each marked with a different letter of the alphabet. What is the probability of being able to spell the word math with four randomly selected tiles that are taken from the bag all at the same time?
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OpenStudy (amistre64):
4/26 id assume
OpenStudy (anonymous):
1/26 * 1/25* 1/24* 1/23 maybe?
OpenStudy (amistre64):
maybe, the questionis an odd read
OpenStudy (anonymous):
4/26 is incorrect
OpenStudy (anonymous):
the answer is 1/ 14950...no idea how
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OpenStudy (amistre64):
cant see where they got that either
OpenStudy (anonymous):
yea but i know its right >.<
OpenStudy (amistre64):
what does "all at the same time" mean ?
OpenStudy (amistre64):
26 group 4?
26P4
----- maybe?
4!
OpenStudy (anonymous):
the tiles are grabbed at once in a handfull
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OpenStudy (anonymous):
hmm
OpenStudy (anonymous):
hmm
OpenStudy (amistre64):
how many ways to group 4 out of 26 is it then
OpenStudy (amistre64):
26.25.24.23
----------- = 14950
4.3.2
OpenStudy (anonymous):
so order of the tiles would matter then?
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OpenStudy (amistre64):
when order matters; use nPr
when grouping matters nCr
OpenStudy (anonymous):
i cant rearange the tiles to spell math in my hand ?
OpenStudy (amistre64):
nPr
--- = nCr
r!
OpenStudy (amistre64):
you simply need an m,t,h,a as a group if you pick them all at once right?
OpenStudy (anonymous):
would i have to pick up the tiles in the specific order, or could i rearange them in my hands?
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OpenStudy (amistre64):
as long as you got the m,a,t,h in your hands; you can spell math
OpenStudy (anonymous):
k yes
OpenStudy (anonymous):
so thenorder wouldnt matter and i would use combinations
OpenStudy (amistre64):
math
mtah
mtha
etc .... are all valid picks
OpenStudy (amistre64):
yep
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OpenStudy (amistre64):
according to the "correct" answer, thats how they solve it
OpenStudy (anonymous):
okay so that 26P4 is invalid?
OpenStudy (amistre64):
26P4 is fine for a start but needs adjusted.
26P4
----- = 26C4
4!
OpenStudy (anonymous):
oh so simple
OpenStudy (anonymous):
thx didnt see it
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OpenStudy (amistre64):
youre welcome; if I didnt see the answer, id a never got it either prolly. Its just an oddly worded question