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Difference between revisions of "AMC 10 2021 (Mock) Problems"

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==Problem 3==
 
==Problem 3==
  
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Let <math>f(1) = 1</math> and <math>f(n) = n dot f(n - 1)</math>.
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Let <math>f(1) = 1</math> and <math>f(n) = n f(n - 1)</math>.

Revision as of 11:25, 29 November 2021

Problem 1

Given that $A + B - C = 2020, B + C - A = 2021,$ and $A + C - B = 2022,$ what is the value of $A + B + C - 2020 - 2021 - 2022$?


$\mathrm{(A) \ } 0\qquad \mathrm{(B) \ } 2020\qquad \mathrm{(C) \ } 2021\qquad \mathrm{(D) \ } 2022\qquad \mathrm{(E) \ } 6063$


Problem 2

A bag of marbles consists of $4$ red marbles and $3$ blue marbles. Each of these $7$ marbles are pulled out one at a time. What is the probability that the $5th$ marble pulled out is red?


$\mathrm{(A) \ } \frac{1}{5}\qquad \mathrm{(B) \ } \frac{3}{7}\qquad \mathrm{(C) \ } \frac{1}{2}\qquad \mathrm{(D) \ } \frac{4}{7}\qquad \mathrm{(E) \ } \frac{4}{5}$


Problem 3

Let $f(1) = 1$ and $f(n) = n f(n - 1)$.

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