A binary number consists only 0s and 1s.
A) How may different seven-digit binary numbers are there?
The first digit cannot be 0, and must be 1.
There is 1 way to choose the first digit.
There are 2 ways to choose the second digit, either 0 or 1.
There are 2 ways to choose the third digit, either 0 or 1.
There are 2 ways to choose the fourth digit, either 0 or 1.
There are 2 ways to choose the fifth digit, either 0 or 1.
There are 2 ways to choose the sixth digit, either 0 or 1.
There are 2 ways to choose the seventh digit, either 0 or 1.
That's 1 = 26 = 64 seven-digit numbers.
B) How may different seven-digit binary numbers are there which begin with a 1
and which contain exactly four 1s.
1 _ _ _ _ _ _
There are 6 positions to place the other 3 1's.
That's 6 positions choose 3 or C(6,3) = 20. We
place 0's in the remaining 3 positions.
Answer: 20
C) How may different seven-digit binary numbers are there which contain exactly
four 1s which are all adjacent(next to each other)?
The first digit must be 1, and since all four 1's must be together,
there is only 1,
1111000
Answer: 1
Edwin
