A store rewards card has a code to identify the user. The code is 6 characters l

Question

A store rewards card has a code to identify the user. The code is 6 characters long and consists of 3 numeric digits, then one uppercase letter and finally 2 more numeric digits. For example: 392H79

a) How many different codes are possible for this store rewards card?

b) What is the probability that last two digits are both odd?

c) What is the probability all the digits are different?

d) What is the probability that the first three digits contain at least 1 even number?

e) What is the probability that first and the fourth digit are the same value? f) What is the probability that the letter is a vowel? (do not consider Y a vowel)

Explanation / Answer

Numbers allowed are 0-9 with no restrication at any position

characters allowed are A-Z with no restrication at any position

(A)

first 3 digits can selected in 10^3 ways

one character can be selected in 26 ways

last 2 digits can be selected in 10^2 ways

Total number of codes possible are 10^3*26*10^2 = 2600000

(B) Probability that las two digits both are odd

first 3 digits can selected in 10^3 ways

one character can be selected in 26 ways

last 2 digits can be selected in 5^2 ways (i.e. odd digits)

Hence total combinations are 10^3*26*5^2

required probability = 10^3*26*5^2 / 10^3*26*10^2 = 25/100 = 1/4

(C)

probability that all digits are different

different codes possible under this condition are 10C1*9C1*8C1*26C1*7C1*6C1

Hence probability = 10*9*8*7*6 * 26 / 10^3*26*10^2 = 0.3024

(D)

there is no even number in first 3 digits, possible selections are = 5^3*26*10^2

P = 5^3*26*10^2/10^3*26*10^2 = 5^3/10^3 = 1/8

required probability = 1-1/8 = 7/8

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