[Math] Probability to win one prize in 5 draws from 100 tickets with one prize for each draw

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Suppose that you hold one of the 100 tickets in a lottery. There are 5 prizes altogether, 1st prize for the first draw, 2nd prize for the second draw, etc. Assume the draws are without replacement. Find the probability that you win one prize.

My attempt:
1/100+1/99+1/98+1/97+1/96.
Not sure if this is correct. Please help

Edit: or would it be $\dfrac{5 \choose 1}{100 \choose 5}$?

Best Answer

Since you hold one ticket, the five prizes must be chosen from the other tickets. Thus the probability that you do not win any prize is $\dfrac{\binom{99}{5}}{\binom{100}{5}}$ and the probability that you win one prize is $1 - \dfrac{\binom{99}{5}}{\binom{100}{5}}$

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