Question

in a lottery daily game, a player picks four numbers from 0 to 9 (without repetition). how many different choices does the player have
a) if order matters?
b) if order does not matter?

Explanation:

Step1: Calculate permutation for part a

When order matters, we use permutation formula \(P(n,r)=\frac{n!}{(n - r)!}\), where \(n = 10\) (numbers from \(0\) to \(9\)), \(r=4\).

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Step2: Calculate combination for part b

When order does not matter, we use combination formula \(C(n,r)=\frac{n!}{r!(n - r)!}\), where \(n = 10\), \(r = 4\).

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Answer:

a) \(5040\)
b) \(210\)