Section 6.2
5. (a) [BB] 9 x 26 x 26 x 26 x 10 x 10 x 10
=
9 . 26
3
.
10
3
=
158,184,000.
(b) [BB] 9 x 26
X
5
=
23,400,000.
(c) [BB] 158,184,000
+
23,400,000
=
181,584,000.
173
6. (a) The first three letters can be chosen arbitrarily, but then last two are determined. So the number of
palindromes is 26
3
=
17,576.
(b) 26
4
=
456,976.
(c) 26
+
26
+
26
2
+
26
2
+
26
3
+
26
3
+
26
4
+
26
4
=
950,508
(d)
26
10
7. (a) [BB] 13 x 6 x 2 x 4
=
624;
8.
(a)
26;
(b) 8;
(c)
36;
(b)[BB] 13
+
4
=
17;
(d) 40.
(c) [BB] 25.
9. [BB]
(a)
4
x
4
=
16;
(b) 4 x 4 x 4
=
64;
(c)
16
+
64
=
80.
10. 8 x 8 x 9 x 10 x 10 x 10 x 10
=
5,760,000
11. [BB] 60 x 60 x 60
=
216,000
12. Choose a row and then one of the seven adjacent pairs of squares in that row, or choose a column and
then one of the seven adjacent pairs of squares in that column. There are 8 x 7
+
8 x 7
=
112 adjacent
pairs of squares.
13. [BB] 500
+
(500)(499)
+
(500)(499)(498)
=
1.24501 x 10
8
14.
(a)
3
x
5
=
15;
(b) 15 x 15
=
225;
(c) 3 x 5 x 4 x 2
=
120.
15. The numbers required are of the form
25x, 52x, 2x5, 5x2, x25
or
x52.
There are seven numbers
of each type since there are seven digits 1, 2, 4, 5, 6, 8, 9 available. By the addition rule, there are
7(6)
=
42 numbers altogether. Not all of these are different, however. When
x
=
2 or
x
=
5, six
numbers are counted twice. So the answer is 42 
6
=
36 numbers.
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This note was uploaded on 11/08/2010 for the course MATH discrete m taught by Professor Any during the Summer '10 term at FSU.
 Summer '10
 any
 Graph Theory

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