Discrete Mathematics Practice Test 6

1. How many numbers must be selected from the set {1, 2, 3, 4} to guarantee that at least one pair of these numbers add up to 7?

2. From a group of 8 men and 6 women, five persons are to be selected to form a committee so that at least 3 women are there on the committee. In how many ways can it be done?

3. The argument of each recursive call is the content of a field of the original output. This definite characteristic belongs to which of the following function?

4. How many numbers of three digits can be formed with digits 1, 3, 5, 7 and 9?

5. Find the odd positive integer of the number 6500.

6. Determine the number of ways of selecting one or more letters from the letters BBBBBB?

7. The code for a safe is of the form PPPQQQQ where P is any number from 0 to 9 and Q represents the letters of the alphabet. How many codes are possible for each of the following cases? Note that the digits and letters of the alphabet can be repeated.

8. There are 15 people in a committee. How many ways are there to group these 15 people into 3, 5, and 4?

9. If the height of a binary tree is 54, how many null pointers are there as children?

10. A drawer contains 12 red and 12 blue socks, all unmatched. A person takes socks out at random in the dark. How many socks must he take out to be sure that he has at least two blue socks?