Help me solve this Probability question

le question :
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the numbers 2, 5 and 7 are written on three cards. one or more of these cards are selected to form a number that consists f a one-,two-, or three-digit number. list the sample space if this experiment ( (a) consist of two digits
(b) is greater than 55
(c) is divisible by 6

please explain with the working
thank you :)

In short, they are asking you to produce all the numbers which can be formed with 2, 5 and 7.

Sample space
= {2, 5, 7, 25, 27, 52, 57, 72, 75, 257, 275, 527, 572, 725, 752}

(a)

P(number consist of two digits)
= 6 / 15
= 3 / 5

From the above sample space, you can see that out of the 15 digits, there are only 6 with two digits.

(b)

P(number formed is greater than 55)
= 9 / 15
= 3 / 5

From the sample space, any number after 57 (as well as 57) is greater than 55.
We have 9 such numbers out of 15 numbers, thus the probability.

(c)

P(number formed is divisible by 6)
= 1 / 15

From the above numbers in the sample space, only 72 is divisible by 6.
To be divisible by 6, a number must be divisible by 2 and 3.
If a number is divisible by 2, it must be even.
If a number is divisible by 3, the sum of its digits must be divisible by 3.
Hence, only 72 is divisible by 3 (Well, you could also use a calculator to check the rest.)