# Math problem.?

In a popular lottery game, five numbers are to be picked randomly from 1 to 36, with no repetition.

a. How many ways can these five numbers be picked without regard to order?

b. Answer the same question for picking six numbers.

Favorite Answer

– Order is not important,

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

– There is no repetition

———————————————————–

(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…)

———————————————————-

(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

——————————————————–

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

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