Discrete mathematics, 1) a) How many 16 bit strings of 0's

Discrete mathematics

Reference no: EM13160432

1)
a) How many 16 bit strings of 0's and 1's contain exactly 7 1's?

b) How many 16 bit strings of 0's and 1's contain at least one 1?

2)
a) How many ways can 2 integers from 1,2,...,100 be selected
so that their sum is even?

b) How many ways can 2 integers from 1,2,...,100 be selected
so that their sum is odd?

3) Calculate the number of integer solutions for the equation

    x₁ + x₂ + x₃ = 20 ,  each x_i ? integer; x_i ? 0;

For ex. one solution is (x₁, x₂, x₃) = (5,7,8)

4) How many integers from 1 to 999 have the sum of their
digits equal to 9?

For ex. the sum of digits in 54, 621, ... are equal to 9.

5) Calculate the number of ways to place 6 identical books
into 9 boxes.

Reference no: EM13160432

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