Question 17407
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,
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