Learning Materials
Features
Discover
Chapter 1: Q. 1.14 (page 16)
How many -card poker hands are there?
Number of -card poker hands.
Over 30 million students worldwide already upgrade their learning with Vaia!
All the tools & learning materials you need for study success - in one app.
Get started for free
Five separate awards (best scholarship, best leadership qualities, and so on) are to be presented to selected students
from a class of . How many different outcomes are possible if
(a) a student can receive any number of awards?
(b) each student can receive at most award?
Delegates from countries, including Russia, France, England, and the United States, are to be seated in a row. How many different seating arrangements are possible if the French and English delegates are to be seated next to each other and the Russian and U.S. delegates are not to be next to each other?
In how many ways can novels, mathematics books, and chemistry book be arranged on a bookshelf if
(a) the books can be arranged in any order?
(b) the mathematics books must be together and the novels must be together?
(c) the novels must be together, but the other books can be arranged in any order?
John, Jim, Jay, and Jack have formed a band consisting of 4 instruments. If each of the boys can play all 4 instruments, how many different arrangements are possible? What if John and Jim can play all 4 instruments, but Jay and Jack can each play only piano and drums?
The following identity is known as Fermat’s combinatorial identity:
Give a combinatorial argument (no computations are needed) to establish this identity.
Hint: Consider the set of numbers through . How many subsets of size have as their highest numbered member?
What do you think about this solution?
We value your feedback to improve our textbook solutions.
Explanations 
Textbooks 
Exams 
GCSE 
IGCSE 
AS 
A Level 
International A Level 
University Admissions Tests 
Flashcards 
Vaia AI 
Notes 
Study Plans 
Study Sets 
Find a job 
Find a degree 
Student Deals 
Magazine 
Mobile App