Chapter 6: Q23E (page 396)
How many positive integers between \(100\) and \(999\) inclusive are divisible by \(3\)and by \(4\) ?
\(75\) integers are divisible by \(3\) and \(4\).
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How many bit strings of length 10contain
a) exactly four 1s?
b) at most four 1s?
c) at least four 1s?
d) an equal number of 0s and 1s ?
a) Derive a formula for the number of permutations ofobjects of k different types, where there are indistinguishable objects of type one, indistinguishable objects of type two,..., and indistinguishable objects of type k.
b) How many ways are there to order the letters of the word INDISCREETNESS?
The internal telephone numbers in the phone system on a campus consist of five digits, with the first digit not equal to zero. How many different numbers can be assigned in this system?
How many positive integers less than \({\rm{1000}}\)
a) have exactly three decimal digits?
b) have an odd number of decimal digits?
c) have at least one decimal digit equal to \({\rm{9}}\)?
d) have no odd decimal digits?
e) have two consecutive decimal digits equal to \({\rm{5}}\)?
f) are palindromes (that is, read the same forward and backward)?
Explain how to find the number of bit strings of length not exceeding 10 that have at least one 0 bit.
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