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# counting

0
32
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How many 4 letter words can be formed using the letters from the word SATURDAY? The words don't have to actually be words.

Sep 9, 2020

#1
+2
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For all the letters in the 4 letter word you can choose from 7 different letters. If we have 4 slots and 7 choices then we get $$4\cdot 7 = \boxed{28}$$

Sep 9, 2020
#2
0

{A, A, D, R} | {A, A, D, S} | {A, A, D, T} | {A, A, D, U} | {A, A, D, Y} | {A, A, R, S} | {A, A, R, T} | {A, A, R, U} | {A, A, R, Y} | {A, A, S, T} | {A, A, S, U} | {A, A, S, Y} | {A, A, T, U} | {A, A, T, Y} | {A, A, U, Y} | {A, D, R, S} | {A, D, R, T} | {A, D, R, U} | {A, D, R, Y} | {A, D, S, T} | {A, D, S, U} | {A, D, S, Y} | {A, D, T, U} | {A, D, T, Y} | {A, D, U, Y} | {A, R, S, T} | {A, R, S, U} | {A, R, S, Y} | {A, R, T, U} | {A, R, T, Y} | {A, R, U, Y} | {A, S, T, U} | {A, S, T, Y} | {A, S, U, Y} | {A, T, U, Y} | {D, R, S, T} | {D, R, S, U} | {D, R, S, Y} | {D, R, T, U} | {D, R, T, Y} | {D, R, U, Y} | {D, S, T, U} | {D, S, T, Y} | {D, S, U, Y} | {D, T, U, Y} | {R, S, T, U} | {R, S, T, Y} | {R, S, U, Y} | {R, T, U, Y} | {S, T, U, Y} = 50 Combinations.

S A T U R D A Y = 8 Letters. It is much easier to list the combinations first and then convert them to permutations. There are: [15 x 4!/2] + [35 x 4!] =180 + 840 =1,020 four-letter permutations or "words".

Sep 9, 2020