A student

A student is to answer 8 out of 10 questions on the exam.
a) find the number n of ways the student can choose 8 out of 10 questions
b) find n if the student must answer the first three questions
c) How many if he must answer at least 4 of the first 5 questions?

Correct result:

a =  45
b =  21
c =  35

Solution:

C8(10)=(108)=10!8!(108)!=10921=45 a=(810)=45
C5(7)=(75)=7!5!(75)!=7621=21 b=(83103)=21
C4(5)=(54)=5!4!(54)!=51=5 C5(5)=(55)=5!5!(55)!=11=1  C3(5)=(53)=5!3!(53)!=5421=10  c=(45) (45)+(55) (53)=(45) (45)+1 10=35



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