Assignment:
Q1. How many permutations of the letters ABCDEFGH contain
a. the string ED?
b. the string CDE?
c. the strings BA and FGH?
d. the strings AB, DE and GH?
e. the strings CAB and BED?
f. the strings BCA and ABF?
Q2. How many ways are there for eight men and five women to stand in a line so that no two women stand next to each other? [Hint: First position the men and then consider possible positions for the women.]
Q3. A coin is flipped 10 times where each flip comes up either heads or tails. How many possible outcomes
a. are there in total?
b. contain exactly two heads?
c. contain at most three tails?
d. contain the same number of heads and tails?
Q4. How many positive integers between 50 and 100
a. are divisible by 7? Which integers are these?
b. are divisible by 11? Which integers are these?
Provide complete and step by step solution for the question and show calculations and use formulas.