Question

"= σ_P² = PQ / n"

How do I use this equation and plug in actual values to figure out the probability of this question:

How many "random" patterns can I make from these five values without repeating numbers within a set, {1,5,10,25,50} ?

Answer 1

In the first part it's given that variance of sample proportion is equal to PQ/n. When P which is population proportion is not known then actual values that is in terms of observed sample proportion p can replace P and Q =1-P

In the second question the given set of 5 numbers can construct random patterns in 5! Ways without repeating any number.

Where 5!=5*4*3*2*1= 120 ways.

Explanation - first place in the pattern can be occupied in 5 ways, because there are 5 numbers, second place can be occupied by remaining 4 numbers in 4 ways and so on we obtaintotal number of ways as 5*4*3*2*1.