Question 17407: How many four letter words can be formed with the word MANAGEMENT?
In the question use the technique where order matters.
Found 2 solutions by AnlytcPhil, crazymaths:
Answer by AnlytcPhil(1806)   (Show Source):
You can put this solution on YOUR website! How many four letter words can be formed with the word MANAGEMENT?
In the question use the technique where order matters.
MANAGEMENT
If the 2 M's, the 2 A's, the 2 N's, and the 2 E's were distinguishable
like this
M1A1N1A2GE1M2E2N2T
the answer would be 10!
However the M's are not distinguishable, so we must divide by 2!
to remove the duplications.
The same can be said about the A's, N's and E's, so we must divide
by 2! for each of these too. The answer is
10! 10×9×8×7×6×5×4×3×2×1
—————————— = —————————————————————— = (after canceling) = 226800
2!2!2!2! 2×2×2×2
Edwin
AnlytcPhil@aol.com
Answer by crazymaths(1)  (Show Source):
You can put this solution on YOUR website! Question:-How many four letter words can be formed with the word MANAGEMENT?
In the question use the technique where order matters.
This is an example of Distinct Permutation.
Ok, the word "MANAGEMENT' contains of 8vowels and 2consonants.
The letters repeating are "A" = 2 times, "M" = 2 times, "N" = 2 times, "E" = 2 times.
Conditions taken into account for solving :-
1> If repetition is allowed, then
10 P 4 --------------> As four letter word is to be formed by 10 letter word
Which is 10*9*8*7=5040
Answer 1:- 5040 -----> If repetition is allowed.
2> If repetition is NOT allowed, then
10 P 4 / 2! * 2! * 2! *2! ----------> Eliminating the repeating elements, A, M, N & E respectively
(2! = 2*1) E.g (5!=5*4*3*2*1) So (2!*2!*2!*2!=2*1 *2*1 *2*1 *2*1 = 16)
Therefore, 5040/16
Answer 2:- 315-----> If repetition is now allowed.
Therefore. there are 315 four letter words that can be formed by letter "M A N A G E M E N T '.
Crazymaths,
Cheers, hope this helps you !!!!!!!!!!!!!
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