SOLUTION: find the number of ways in which an arrangement of of 4 letters can be made from the word MATHEMATICS a)1680 b)756 c)18 d)2454

Algebra ->  Permutations -> SOLUTION: find the number of ways in which an arrangement of of 4 letters can be made from the word MATHEMATICS a)1680 b)756 c)18 d)2454      Log On


   

Question 333411: find the number of ways in which an arrangement of of 4 letters can be made from the word MATHEMATICS
a)1680
b)756
c)18
d)2454
Answer by jrfrunner(365) About Me  (Show Source):
You can put this solution on YOUR website!
while the word MATHEMATICS has 11 words, there are really only 8 unique words
M, A and T are duplicated.
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So, your problem becomes number of arrangements of 4 letters from a word of 8 unique letters
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there are 8 choices for the first word
there are then 7 choices for the second word
after that there are 6 choices for the third word
and finally there are 5 choices for the fourth word
8*7*6*5=1680