```ORGANIZED COUNTING
1.
2.
3.
4.
5.
Four different math texts and three different English texts are arranged in a row on a shelf.
Determine the number of ways the texts can be arranged if:
a)
the texts are alternated by subject;
[144]
b)
the math texts are grouped together and
the English texts are grouped together.
[288]
Determine the number of ways 8 math teachers can sit around a circular table if:
a)
Mr. Colavecchio can’t sit beside Mr. Pisocky;
[3600]
b)
Mrs. Peleck must sit across from Ms. DiIorio and
Mrs. McCarthy must sit across from Ms. Nestico.
[144]
Determine the number of arrangements possible using the letters of the word FERMAT if:
a)
all the letters are used and there are no restrictions;
[720]
b)
all the letters are used and the arrangements must end in a vowel;
[240]
c)
only 5 letters are used;
[720]
d)
only 5 letters are used but the first one must be a T and the arrangement
must end in a vowel.
[48]
Determine the number of 4-digit numbers that can be formed if:
a)
there are no restrictions;
[9000]
b)
all of the digits are different;
[4536]
c)
all of the digits are different and the number 21
is contained somewhere in the arrangement.
[154]
Determine the number of odd 4-digit numbers that can be formed using the digits
0 to 8 if there must be a 5 in the number and no digit may be repeated.
[636]
```