1. How many 12-bit strings (that is, bit strings of length 14)
start with the sub-string 011?
2. You break your piggy bank to discover lots of pennies and
nickels.
You start arranging them in rows of 6 coins.
How many coins would you need to make all possible rows of 6
coins (not necessarily with equal numbers
of pennies and nickels)?
3. How many shortest lattice paths start at (4, 4) and end at
(13, 13)?
4. What is...
How many bit strings of length 8 if i. bit strings start with
the bit 1; ii. bit strings end with the two bits 00; iii. bit
strings either start with the bit 1 or end with the bits 00.؟
Recall that a 5-bit string is a bit strings of length
5, and a bit string of weight 3, say, is one with exactly three
1’s.
a. How many 5-bit strings are there?
b. How many 5-bit strings have weight 0?
c. How many 5-bit strings have weight 1?
d. How many 5-bit strings have weight 2?
e. How many 5-bit strings have weight 4?
f. How many 5-bit strings have weight 5?
g. How many 5-bit strings have weight...
This is one question about 14-bit strings
How many 14-bit strings that have more 0’s than 1’s?
How many 14-bit strings that have even number of 0’s?
How many 14-bit strings that have no consecutive three 0’s in a
row?
Suppose that you pick a bit string
from the set of all bit strings of length ten. Find the probability
that
the bit string has exactly two 1s;
the bit string begins and ends with 0;
the bit string has the sum of its digits equal to seven;
the bit string has more 0s than 1s;
the bit string has exactly two 1s, given that the string begins
with a 1.
Suppose that you pick a bit string from the set of all bit
strings of length ten. Find the probability that
the bit string has exactly two 1s;
the bit string begins and ends with 0;
the bit string has the sum of its digits equal to seven;
the bit string has more 0s than 1s;
the bit string has exactly two 1s, given that the string begins
with a 1.
Problem 33.2ish. How many strings of fourteen
lowercase English letters are there which
(a) start with the letter x, if letters may be repeated?
(b) contain the letter x at least once, if letters can be
repeated?
(c) contain each of the letters x and y at least once, if
letters can be repeated?
(d) which contain at least one vowel, where letters may not be
repeated?