2： There are 2 mathcounts (mock) problems among us

A quick reminder of what a factorial is:
5!=5*4*3*2*1, 20!=20*19*...*1

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What is $$\frac{2024!}{2023!}$$ ?

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How many trailing zeroes (consecutive zeroes at the end of a number) are there in $$2^5\cdot3^3\cdot7^2\cdot5^4$$ ?

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$$\frac{50!}{5^x}$$ yields an integer. What is the maximum possible integer value of $$x$$ ? In other words, how many times can you divide 50! by 5 until you get a fraction?

(Try prime factorizing it while ignoring the stuff that doesn't matter!)

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How many trailing zeroes are at the end of $$\left(\frac{20!}{17!}\right)!$$ ?

Reminder on infinite geometric series

Multiple Choice

What is $$\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}...$$

• 31/32

• 1

• 99

• 15/16

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Al and Brenda are bored, and decide to play a game. They each take turns tossing an unfair coin, with probability of landing heads 1/6th of the time and tails 5/6ths of the time. They each keep on tossing the coin until one of them tosses a head, resulting in them winning the game. Al goes first. What is the chance Al wins on the first or second toss?

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What's the probability that Al wins? Express your answer as a common fraction. (Same rules as before, 1/6 chance heads, 5/6 chance tails, Al goes first, if heads then win)

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