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# Basic probability

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A number is chosen at random from the set of consecutive natural numbers $\{1, 2, 3, \ldots, 24\}$. What is the probability that the number chosen is a factor of $4!$? Express your answer as a common fraction.

Apr 6, 2020

### 3+0 Answers

#1
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4!=24

The factors of 24 are 1,2,3,4,6,8,12,24 and there are 8 of them

Therefore there is an $$\frac{8}{24}$$ or $$\frac{1}{3}$$ chance that the number chosen is a factor of 4!

Hope this helps!

-Ako

Apr 6, 2020
#2
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In 4 factorial , it is 1*2*3*4 which factorizes to 2^3*3. This means is has 8 factors: 1,2,3,4,6,8,12, and 24. If a number is randomly chosen from 1-24, 8 out of the 24 would be factors of 4!. That means your answer will be 8/24=1/3.

Hope it helps!

Apr 6, 2020
#3
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thx both of u

Apr 6, 2020