3. 5. How many different quot;wordsquot; can be made from the letters
in quot;teacherquot; if...
a) all letters are used?
b) only 4 letters are used?
3
4. 5. How many different quot;wordsquot; can be made from the letters
in quot;teacherquot; if...
a) all of the letters are used?
T E A C H E R
7 6 5 4 3 2 1
_
= 7!
2!
= ___
5040
2
= 2520
4
5. 5. How many different quot;wordsquot; can be made from the letters
in quot;teacherquot; if...
there are 7
a) all of the letters are used? letters all in
total.
T E A C H E R
7 6 5 4 3 2 1
_
= 7! dividing by 2 factorial because
2!
there is a letter that is doubled
= ___ which is the quot;Equot;'s.
5040
2
= 2520
5
6. 5. How many different quot;wordsquot; can be made from the letters
in quot;teacherquot; if...
b) only 4 letters are used?
total letters = 7
T E A C H E R
EE TCHRA
no E's and 4 other letters and arrange
Case 1.
6
7. Case 2.
1 E and 3 other letters and arrange then divide reps.
7
8. Case 3.
2 E's and 2 other letters and arrange and divide reps.
8
9. 5. How many different quot;wordsquot; can be made from the letters
in quot;teacherquot; if...
b) only 4 letters are used?
total letters = 7
T E A C H E R
EE TCHRA The letter's that don't have
repititions, meaning any repititions, meaning there
where there is double isn't any doubles of each
letters. in this case, letter. such as, there's only 1
there are 2 E's. t, c, h, r, and a in the word
quot;teacherquot;.
9
10. no E's and 4 other letters and arrange
Case 1.
where there is 5 letter's that doesn't
have any reps, i'll be chosing 4 out of
those 5 letters.
finally, we have
where there are 2 E's and which ourselves our 4 letters
in this case i will only be
that will only be used
chosing 4 letters that will not be
from the word quot;teacherquot;
E
10
11. Case 2. 1 E and 3 other letters and arrange then divide reps.
i'll be chosing 1 letter E to be one of my 4
letters that are going to be used, and that
leaves me with 3 letters left and then i divide
by the reps which is 2, since there's 2 E's in
quot;teacherquot;
11
12. Case 2. 1 E and 3 other letters and arrange then divide reps.
there are 5 letters that dont
finally, i have 4 letters
have any reps, and im
that i'll be chosing then
chosing 3 out of those 5
i divide by 2, since
letters.
there's only a set of E's
2 E's to chose from and i'm only
that only repeats itself,
going to chose 1 out of the 2 E's
meaning there's only 2
E's
12
13. Case 3. 2 E's and 2 other letters and arrange and divide reps.
in this case, i'll be chosing all the E's, and all i need left is 2 more
other letter to make that 4 letters that im going to use.
finally have 4 letters
that will only be
2 chose 2 meaning, i'll there are 5 letters from used and then divide
the non rep letters which
be chosing all of the by 2 factorial
i haven't still chose from,
E's since there's only 2
and chosing 2 from out
of them anyways.
of those 5 letters.
13