Answer to Question #218097 in Discrete Mathematics for Dave

Question

1.     Three departmental committees have 6, 12, and 9 members with no overlapping membership. In how many ways can these committees send one member to meet with the president?

2.     Two dice are rolled, one blue and one red. How many outcomes give the sum of 5 or the sum of 9?

3.     The options available on a particular model of a car are five interior colors, six exterior colors, two types of seats, three types of engines, and three types of radios. How many different possibilities are available to the consumer?

4.     Two dice are rolled, one blue and one red. How many outcomes are possible?

5.     How many times is How many eight-bit strings read the same from either end? (An example of such an eight-bit string is 01111110. Such strings are called palindromes.)

Answer 1

Solution.

1. According to the addition principle, these committees can send one member to meet with the president using 6+12+9=27 ways.

2. There are 4 ways for the two dice to give a sum of 5: 1+4, 2+3, 3+2, 4+1.

There are 4 ways for the two dice to give a sum of 9: 3+6, 4+5, 5+4, 6+3.

Therefore there are 8 (4+4)

ways as a rule of sum to get a sum of 5

or 9.

3. 5•6•2•3•3=540 different possibilities are available to the consumer.

4. There are 6 possible results for the red sided die, the same situation with blue sided die.

So 6*6=36 options.

5.

Since the strings read the same from either end, this means that the first 4 bits of the 8-bits string uniquely determine the string. Еach bit can be selected in 2 ways. So 2*2*2*2=16. We have

16 strings.