A contest consists of predicting the results (win, draw or defeat) of 10 football matches. Then the number of ways in which one entry contains at least 5 correct answers is:
Options:
Answers
3¹⁰ - ∑ ¹⁰Cₙ(1)ⁿ2¹⁰⁻ⁿ n from 0 to 4
Step-by-step explanation:
A contest consists of predicting the results (win, draw or defeat) of 10 football matches
Total possible event = 3¹⁰
the number of ways in which one entry contains at least 5 correct answers is
= Total possible event - Less than 5 Correct Answers
Less than 5 Correct Answers = 0 , 1 , 2 , 3 , 4 Correct answers
= ¹⁰C₀(1)⁰2¹⁰ + ¹⁰C₁(1)¹2⁹ + ¹⁰C₂(1)²2⁸ + ¹⁰C₃(1)³2⁷ + ¹⁰C₄(1)⁴2⁶
= ∑ ¹⁰Cₙ(1)ⁿ2¹⁰⁻ⁿ n from 0 to 4
the number of ways in which one entry contains at least 5 correct answers is = 3¹⁰ - ∑ ¹⁰Cₙ(1)ⁿ2¹⁰⁻ⁿ n from 0 to 4
option 2 is correct
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