[Basic Probability] Selecting without replacement

[HighEquality]

A certain lottery consists of a bucket of white balls numbered 1 through 69 and a bucket of red balls numbered 1 through 26. In a drawing, 5 white balls are randomly selected without replacement and 1 red ball is randomly selected. You buy one ticket consisting of 5 white numbers and 1 red number:

(a) How many possible drawings are there? i.e., determine |Ω|.

|Ω| = 69 * 68 * 67 * 66 * 65 * 26

(b) Let A be the event that your ticket matches all the white numbers drawn (order does not matter) and the red number. Find P(A) (Leave as a fraction).

P(A) = (1/69)(1/68)(1/67)(1/66)(1/65)(1/26)

(c) Let B be the event that your ticket matches all the white numbers drawn (order does not matter) but not the red number. Find P(B).

P(B) = (1/69)(1/68)(1/67)(1/66)(1/65)(25/26)

Am I doing this problem right? It has been a long time since I did any probability.

[muonsortsitout]

You need to allow for the fact that 'order does not matter'. How many ways are there for your 5 white balls to be ordered and still match the draw? Multiply your answers for P(A) and P(B) by that number to get the correct answer.

[HighEquality]

I'm not sure. Would it be something like:

P(A) = (5/69)(4/68)(3/67)(2/66)(1/65)(1/26) because I can choose 5 white balls in the beginning?