Please answer all questions and explain how you got the answer!!! when choosing

Question

Please answer all questions and explain how you got the answer!!!

when choosing 6 cards from a standard deck of cards, what is the probability you get only hearts? enter numeric values for numerator and denominator.

what is the probability you guess the 4 digit pin on my ATM card on the first try? enter answer as a fraction.

car license plates in CA have 1 digit, 3 letters, then 3 more digits. what is the probability you guess the license plate on mrs chos car? give both the fraction and decimal rounded answer to one non zero digit.

Explanation / Answer

a) P(all are hearts) = 13C6 / 52C6 = 1716 / 20358520

b) Total number of digits 10 since 0,1,2,3,...,9

P(you guess the 4 digit pin on my ATM Card on the first try) = 1 / 104 = 0.0001

c) Choose 1 digit in 10 ways, 3 letters are chosen in 26^3 = 17576 since 26 letters, then choose 3 more digits 10^3. = 1000

The probability you guess the license plate on mrs chos car is 1 / (10*17576 * 1000) = 1 / 175760000

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