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 five questions?

Correct answer:

a =  45
b =  21
c =  35

Step-by-step explanation:

C8(10)=(810)=8!(108)!10!=21109=45 a=(108)=45
C5(7)=(57)=5!(75)!7!=2176=21 b=(10383)=21
C4(5)=(45)=4!(54)!5!=15=5 C5(5)=(55)=5!(55)!5!=11=1  C3(5)=(35)=3!(53)!5!=2154=10  c=(54) (54)+(55) (35)=(54) (54)+1 10=35

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