Permutations and Combinations Help- Cambridge (1 Viewer)

[bleh1234]

Find how many arrangements there are of the letters of the word GUMTREE if
a) the G is somewhere between the two Es
b) the M is somewhere to the left of both Es and the U is somewhere between them
c) the G is somewhere to the left of the U and the M is somewhere to the right of the U
Thanks in advance!
The answers are:
a)840
b) 210
c)420

 

[BLIT2014]

Formula:
= r(n-1Pr-1)

a)
(7P5/4P2)*4=840


b) 7P5/4P2=210

c) 7P5/4P2*2=420

 

[braintic]

TOTAL number of arrangements = 7!/2! = 2520.

(a) Ignoring the other letters, the only arrangements for the G, E, E are: GEE, EGE, EEG
So one third of all arrangements have the G between the Es, ie. 840

(b) Number of 'words' using MUEE is 4!/2! = 12.
We want MEUE - ONE of the 12 possibilities.
One 12th of 2520 is 210.

(c) There are 3! = 6 ways of arranging G, U, M.
We want GUM - ONE of the 6 arrangements.
1/6 of 2520 is 420

 

[bleh1234]

Thank you so much braintic Awesome explanation!

 

[eeeeeeeeeeeqwe]

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