In a lottery,a person chooses six different n | vedclass

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(A) The total number of ways to choose $6$ different numbers from $20$ is given by the combination formula $^{n}C_{r} = \frac{n!}{r!(n-r)!}$.Total way

Vedclass · Accepted Answer

$\frac{1}{38760}$

Vedclass · Answer

(A) The total number of ways to choose $6$ different numbers from $20$ is given by the combination formula $^{n}C_{r} = \frac{n!}{r!(n-r)!}$.Total ways $= ^{20}C_{6} = \frac{20!}{6! 	imes 14!} = \frac{20 	imes 19 	imes 18 	imes 17 	imes 16 	imes 15}{6 	imes 5 	imes 4 	imes 3 	imes 2 	imes 1} = 38760$.Since only one specific combination of $6$ numbers is fixed by the lottery committee,there is only $1$ favorable outcome.Therefore,the probability of winning the prize is $\frac{	ext{Favorable outcomes}}{	ext{Total outcomes}} = \frac{1}{38760}$.

In a lottery,a person chooses six different natural numbers at random from $1$ to $20$. If these six numbers match the six numbers already fixed by the lottery committee,he wins the prize. What is the probability of winning the prize in the game? [Hint: The order of the numbers is not important.]

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