# In a certain​ lottery, you must select 5 numbers​ (in any​ order) out of 33 correctly...

In a certain​ lottery, you must select 5 numbers​ (in any​ order) out of 33 correctly to win.

a. How many ways can 5 numbers be chosen out of 33 ​numbers?

b. You purchase one lottery ticket. What is the probability of​ winning?

Solution:- by using above data
Use that combination with n = 33 and r = 5

a. definition Combination Cn,r = n!/r!(n-r)!

33C5 = 33!/(33!*28!) = 237336

b. The probability of winning one lottery ticket = 0.00000421
P(win) = number of favorable outcomes/number of possible outcomes
= 1/237336
= 0.00000421

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