MULTIPLE CHOICE QUIZ.. BUT PLEASE EVALUATE FOR FULL CREDIT!! DISCRETE MATHEMATIC

Question

MULTIPLE CHOICE QUIZ.. BUT PLEASE EVALUATE FOR FULL CREDIT!!

DISCRETE MATHEMATICS - PERMUTATION, COMBINATIONS, COLLECTIONS

1. The number of positive integers less than or equal to 300 that are divisible by at least one of the number 5, 6, 15 is: A. 110 B. 100 C. 120 D. 150 E. NONE OF THE ABOVE

2. How many functions f from {1, 2, 3, 4} to {1, 2, 3, 4, 5, 6} such that f(i) ? {2, 3} for i = 1, 2? A. 36 B. 64 C. 72 D. 48 E. NONE OF THE ABOVE

3. Let X be a set of positive integers of size at least 2. What is the smallest size of X that
will guarantee there are two distinct members of X such that either their sum or their
difference is divisible by 10? A. 7 B. 6 C. 10 D. 5 E. NONE OF THE ABOVE

4. Suppose there are 3 pairs of white, 4 pairs of grey and 5 pairs of black socks in a drawer.
The least number of socks to be chosen so that one can guarantee that there are two
matching pairs (the two pairs need not have the same color)
A. 5 B. 8 C. 6 D. 12 E. NONE OF THE ABOVE

5. Find the number of ways of forming a team of 10 students from
a large university (i.e. you are assume there are more than 10 students in each group) to
represent freshman, sophomores, juniors, seniors, and graduate students such that at least two from each group.
A. C(4, 4) B. C(10, 2) C. C(5, 2) D. (C(5, 1))2 E. NONE OF THE ABOVE

6. Suppose there are 17 students. Find the number of ways of partitioning them into four groups of equal size and a group with smaller size.
A. C(17; 4, 4, 4, 4)/4! B. C(17; 4, 4, 4, 4) C. C(17, 4)^4 D. (17) ? C(16, 4)^4 E. NONE OF THE ABOVE

7. Suppose there are 17 students. Find the number of ways of partitioning them into two groups of 5 students and one group of 7 students.   A. C(17; 5, 5, 7) B. C(17; 5, 5, 7)/(5!) C. C(17; 5, 5, 7)/(5!)^2 D. C(17; 5, 5, 7)/(7!) E. NONE OF THE ABOVE

Explanation / Answer

1. since multiple of contain 15, so it can be ignored. also in multiple of 6 only 30, 60, 90,120.150,180,210,240,270,300 are common in multiple of 5.

so, (B). 100

6. 17C16 *16C4 *12C4 *8C4 *4C4 *1C1

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