Section 7.2
185
16. (a) [BB] 9 x 9 x 8 x 7 x 6 x 5 x 4
=
9 x
P(9,6)
=
9 x 60,480
=
544,320.
(b) The total number of 7 digit numbers which do not contain a 6 is 8 x 8 x 7 x 6 x 5 x 4 x 3
=
161,280.
The number which contain neither a 3 nor a 6 is 7 x 7 x 6 x 5 x 4 x 3 x 2
=
35,280. Hence, the
answer is 161,280 
35,280
=
126,000.
17. (a)
P(9,7)
=
9 x 8 x 7 x 6 x 5 x 4 x 3
=
181,440.
(b) [BB] There are seven available positions for the 3, then six for the 6, then five for the remaining
seven digits. The answer is 7 x 6 x
P(7,
5)
=
42 x 2520
=
105,840.
(c) There are six pairs of consecutive positions into each of which we can place 36 or 63. After this,
there remain five positions to be filled from the remaining seven digits. The answer is 6 x 2 x
P(7,5)
=
30,240.
(d) [BB] There are seven digits to be placed in seven positions. The answer is
P(7,
7)
=
5040.
(e) There are seven positions for the 3, then seven numbers to be placed in six positions. The answer
is 7 x
P(7,6)
=
35,280.
(t) Using the result of the previous part, 35280
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 Summer '10
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 Graph Theory, Idaho, Nebraska, Basic concepts in set theory, seven digits, 7digit

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