– Order is not important,

– Each number is distinct (independent of one another),

– There is no repetition

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(a)

Apply the multiplicative rule:

The number of ways in which five numbers can be picked is:

(36 nPr 5)

= 36 * 35 * 34 * 33 * 32 = 45,239,040 ways

(The reason being that initially you have 36 choices, after one is removed and not replaced, you’re left with 35 choices, after another is picked, you’re left with 34 choices, and so on…)

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(b)

Similar to (a), apply the multiplicative rule:

The number of ways in which six numbers can be picked is:

(36 nPr 6)

= 36 * 35 * 34 * 33 * 32 * 31 = 1,402,410,240 ways

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Regarding your additional details, I don’t really see a need to divide by 5!.