a certain lottery requires players to select 7 different numbers, in any order, from 1 to 52 inclusive. how many different sets of 7 numbers can be chosen?

the 7 numbers can be chosen in different ways.
(simplify your answer. type an integer or a fraction.)

Question

a certain lottery requires players to select 7 different numbers, in any order, from 1 to 52 inclusive. how many different sets of 7 numbers can be chosen?

the 7 numbers can be chosen in   different ways.
(simplify your answer. type an integer or a fraction.)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Combinations Formula", "Combinatorics" ], "new_concepts": [], "current_concepts": [ "Combinations Formula", "Combinatorics" ] } ## Identify the parameters for the combinations formula $$ \begin{aligned} &n = 52 \ &r = 7 \end{aligned} $$ ## Apply the combinations formula $$ \begin{aligned} \binom{n}{r} &= \frac{n!}{r!(n-r)!} \ \binom{52}{7} &= \frac{52!}{7! \cdot 45!} \end{aligned} $$ ## Calculate the final value $$ \begin{aligned} \binom{52}{7} &= \frac{52 \times 51 \times 50 \times 49 \times 48 \times 47 \times 46}{7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1} \ &= 133,784,560 \end{aligned} $$ A certain lottery requires players to select 7 different numbers, in any order, from 1 to 52 inclusive. How many different sets of 7 numbers can be chosen? The 7 numbers can be chosen in 133,784,560 different ways. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "Combinatorics" ] }

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Question

Explanation:

Identify the parameters for the combinations formula

Apply the combinations formula

Calculate the final value

Answer: