مؤسسة الرياض الخيرية للعلوم
Riyadh Philanthropic Society For Science
جامعة األمير سلطان
Prince Sultan University قسم علوم الحاسب والمعلومات
Dept. of Computer & Information Sciences
Wednesday, March 31st, 2021
CS 285 – Discrete Mathematics Quiz #5
Student Name Student Id
Answer the following questions and show your work:
1. (4 Marks) Answer the following questions:
a. How many possible combinations of 9 bits string that start with 11 and end with 01 can we
have?
b. How many possible combinations of 9 bits string that start with 01 or end with 001 can we
have?
c. How many possible license plates can we construct if the plate consists of three letters and
four numbers (0 to 9), assume that the alphabet has 24 letters?
d. How many possible license plates can we construct if the plate consists of three letters and
four numbers, no letter can be repeated and zero is not allowed, assume that the alphabet
has 24 letters?
, 2. (3 Marks) Write the expansion of (3𝑥 − 2𝑦)7
3. (2 Marks) What is the coefficient of the 𝑥 13 𝑦14 term in the expansion of
(4𝑥 − 2𝑦)27
2
Riyadh Philanthropic Society For Science
جامعة األمير سلطان
Prince Sultan University قسم علوم الحاسب والمعلومات
Dept. of Computer & Information Sciences
Wednesday, March 31st, 2021
CS 285 – Discrete Mathematics Quiz #5
Student Name Student Id
Answer the following questions and show your work:
1. (4 Marks) Answer the following questions:
a. How many possible combinations of 9 bits string that start with 11 and end with 01 can we
have?
b. How many possible combinations of 9 bits string that start with 01 or end with 001 can we
have?
c. How many possible license plates can we construct if the plate consists of three letters and
four numbers (0 to 9), assume that the alphabet has 24 letters?
d. How many possible license plates can we construct if the plate consists of three letters and
four numbers, no letter can be repeated and zero is not allowed, assume that the alphabet
has 24 letters?
, 2. (3 Marks) Write the expansion of (3𝑥 − 2𝑦)7
3. (2 Marks) What is the coefficient of the 𝑥 13 𝑦14 term in the expansion of
(4𝑥 − 2𝑦)27
2
