Probability Examples Related to Combinations Data Science and A.I. Lecture Series Author: Bindeshwar Singh Kushwaha Example: Drawing Two Cards from a Well-Shuffled Pack of Cards Find the probability of the following scenarios: One red and one black card. Both cards of the same suit. One jack and one king. One red card and one card […]
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Examples and Theorem Related to Combinations Data Science and A.I. Lecture Series Author: Bindeshwar Singh Kushwaha Theorem: Relationship Between Permutations and Combinations Theorem: The number of permutations of \(n\) different objects taken \(r\) at a time is related to the number of combinations by: \[ P^n_r = C^n_r \cdot r! \] where \(0 < r
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Understand Combinations Data Science and A.I. Lecture Series Introduction to Combinations A combination is a selection of items where the order does not matter. Example: Selecting 2 players from a group of 3 players (X, Y, Z). Possible combinations: XY, XZ, YZ. Formula for combinations: \[ \binom{n}{r} = \frac{n!}{r!(n-r)!}, \quad 0 \leq r \leq
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Permutations and Their Theorems Data Science and A.I. Lecture Series Author: Bindeshwar Singh Kushwaha Institute: PostNetwork Academy Theorem 1: Permutations of Distinct Objects The number of permutations of n different objects taken r at a time is: \[ P(n, r) = \frac{n!}{(n-r)!} \] Explanation: First position: n choices. Second position: n-1 choices. Continue until the
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Understanding Permutations Data Science and A.I. Lecture Series Author: Bindeshwar Singh Kushwaha PostNetwork Academy Introduction to Permutations A permutation is an arrangement of objects in a specific order. The order of arrangement is crucial in permutations. Example: Arranging the letters of the word “ABC”. Total permutations = $3! = 6$. Key Formula for Permutations The
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Fundamental Principle of Counting Subtitle: Data Science and A.I. Lecture Series Fundamental Principle of Counting Statement: If one event can occur in m ways and another event can occur in n ways, then the two events together can occur in m × n ways. This principle can be extended to multiple events. For example:Total ways
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