〈6.3.b〉 Practice on Miscellaneous Counting

[Math Center] 1. A certain store sells two types of pens: one type for $[latex]2[latex] per pen and the other type for $[latex]3[latex] per pen. If a customer can spend up to $[latex]25[latex] to buy pens at the store and there is no sales tax, what is the greatest number of pens the customer can […]

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〈6.2.b〉 āĻ¸āĻŽā§āĻ­āĻŦā§āĻ¯āĻ¤āĻž āĻŦāĻŋāĻˇā§ŸāĻ• āĻĒā§āĻ°ā§āĻ¯āĻžāĻ•āĻŸāĻŋāĻ¸

[Math Center] 1. Consider an experiment with events [latex]A, B[latex], and [latex]C[latex] for which [latex]P(A)=0.23,P (B)=0.40, P(C)=0.85[latex], and Suppose that events [latex]A[latex] and [latex]B[latex] are mutually exclusive and events [latex]B[latex] and [latex]C[latex] are independent. What are the probabilities [latex]P(AorB)[latex] and [latex]P(BorC)[latex]?     2. In a box of [latex]10[latex] electrical parts, [latex]2[latex] are defective. (a) […]

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〈6.1.b〉 āĻŦāĻŋāĻ¨ā§āĻ¯āĻžāĻ¸ āĻ“ āĻ¸āĻŽāĻžāĻŦā§‡āĻļ āĻŦāĻŋāĻˇā§ŸāĻ• āĻĒā§āĻ°ā§āĻ¯āĻžāĻ•āĻŸāĻŋāĻ¸

[Math Center] 1. In how many different ways can the letters in the word STUDY be ordered?     2. Martha invited [latex]4[latex] friends to go with her to the movies. There are [latex]120[latex] different ways in which they can sit together in a row of [latex]5[latex]  seats, one person per seat. In how many […]

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〈6.2.a〉āĻ¸āĻŽā§āĻ­āĻŦā§āĻ¯āĻ¤āĻž

 [Math Center Home] [āĻ¨ā§‹āĻŸāĻƒ āĻāĻ‡ āĻ†āĻ°ā§āĻŸāĻŋāĻ•ā§‡āĻ˛āĻŸāĻŋ (6) Counting and Probability āĻŦāĻŋāĻ­āĻžāĻ—ā§‡āĻ°Â āĻ…āĻ§ā§€āĻ¨ā§‡Â ã€ˆ2〉Probability āĻšā§āĻ¯āĻžāĻĒā§āĻŸāĻžāĻ°ā§‡āĻ° āĻ…āĻ¨ā§āĻ¤āĻ°ā§āĻ—āĻ¤, āĻ¯āĻžÂ ã€ˆ6.2.a〉āĻšāĻŋāĻšā§āĻ¨ āĻĻāĻŋā§Ÿā§‡ āĻĒā§āĻ°āĻ•āĻžāĻļ āĻ•āĻ°āĻž āĻšā§Ÿā§‡āĻ›ā§‡] 〈6.2.a〉āĻ¸āĻŽā§āĻ­āĻŦā§āĻ¯āĻ¤āĻž Probability is a quantity that expresses the chance, or likelihood, of an event. In other words, it measures how often an event will occur in a long series of repeated trials. For events with countable outcomes, probability […]

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〈6.3〉Miscellaneous Counting

 [Math Center Home] [āĻ¨ā§‹āĻŸāĻƒ āĻāĻ‡ āĻ†āĻ°ā§āĻŸāĻŋāĻ•ā§‡āĻ˛āĻŸāĻŋ (6) Counting and Probability āĻŦāĻŋāĻ­āĻžāĻ—ā§‡āĻ°Â āĻ…āĻ§ā§€āĻ¨ā§‡Â ã€ˆ3〉Miscellaneous Counting āĻšā§āĻ¯āĻžāĻĒā§āĻŸāĻžāĻ°ā§‡āĻ° āĻ…āĻ¨ā§āĻ¤āĻ°ā§āĻ—āĻ¤, āĻ¯āĻžÂ ã€ˆ6.3.a〉āĻšāĻŋāĻšā§āĻ¨ āĻĻāĻŋā§Ÿā§‡ āĻĒā§āĻ°āĻ•āĻžāĻļ āĻ•āĻ°āĻž āĻšā§Ÿā§‡āĻ›ā§‡] Combinatorics āĻ•āĻŽāĻŦāĻŋāĻ¨ā§‡āĻŸā§‹āĻ°āĻŋāĻ•ā§āĻ¸ āĻšāĻ˛ā§‹ āĻāĻ•āĻŸā§ āĻ•āĻ āĻŋāĻ¨ āĻ§āĻžāĻšā§‡āĻ° āĻ…āĻ‚āĻ•, āĻ¯ā§‡āĻ–āĻžāĻ¨ā§‡ āĻŽā§‚āĻ˛āĻ¤: āĻ¸ā§āĻŸā§āĻĄā§‡āĻ¨ā§āĻŸāĻĻā§‡āĻ° āĻ—āĻŖāĻ¨āĻžāĻ° āĻĻāĻ•ā§āĻˇāĻ¤āĻž āĻ¯āĻžāĻšāĻžāĻ‡ āĻ•āĻ°āĻž āĻšā§ŸāĨ¤ āĻ āĻ§āĻ°āĻŖā§‡āĻ° āĻ…āĻ™ā§āĻ• āĻĒāĻ°ā§€āĻ•ā§āĻˇāĻžā§Ÿ āĻāĻ•āĻŸā§ āĻ•āĻŽ āĻ†āĻ¸āĻ¤ā§‡ āĻĻā§‡āĻ–āĻž āĻ—ā§‡āĻ˛ā§‡āĻ“ āĻ†āĻŽāĻ°āĻž āĻšāĻžāĻ‡ āĻ†āĻĒāĻ¨āĻžāĻ°āĻž āĻ¸āĻ°ā§āĻŦā§‡āĻžāĻšā§āĻš āĻĒā§āĻ°āĻ¸ā§āĻ¤ā§āĻ¤āĻŋāĻ° āĻ¸ā§āĻŦāĻžāĻ°ā§āĻĨā§‡ āĻ•āĻŽāĻŦāĻŋāĻ¨ā§‡āĻŸā§‹āĻ°āĻŋāĻ•ā§āĻ¸ā§‡āĻ° āĻ…āĻ™ā§āĻ•āĻ—ā§āĻ˛ā§‹ āĻ¸āĻŽā§āĻĒāĻ°ā§āĻ•ā§‡ āĻ­āĻžāĻ˛ā§‹ āĻ§āĻžāĻ°āĻŖāĻž āĻ°āĻžāĻ–ā§‡āĻ¨āĨ¤Â āĻ•āĻŽāĻŦāĻŋāĻ¨ā§‡āĻŸā§‹āĻ°āĻŋāĻ•ā§āĻ¸ āĻ•ā§€, […]

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〈6.1.a〉āĻŦāĻŋāĻ¨ā§āĻ¯āĻžāĻ¸ āĻ“ āĻ¸āĻŽāĻžāĻŦā§‡āĻļ

 [Math Center Home] [āĻ¨ā§‹āĻŸāĻƒ āĻāĻ‡ āĻ†āĻ°ā§āĻŸāĻŋāĻ•ā§‡āĻ˛āĻŸāĻŋ (6) Counting and Probability āĻŦāĻŋāĻ­āĻžāĻ—ā§‡āĻ°Â āĻ…āĻ§ā§€āĻ¨ā§‡Â ã€ˆ1〉Permutation and Combination āĻšā§āĻ¯āĻžāĻĒā§āĻŸāĻžāĻ°ā§‡āĻ° āĻ…āĻ¨ā§āĻ¤āĻ°ā§āĻ—āĻ¤, āĻ¯āĻžÂ ã€ˆ6.1.a〉āĻšāĻŋāĻšā§āĻ¨ āĻĻāĻŋā§Ÿā§‡ āĻĒā§āĻ°āĻ•āĻžāĻļ āĻ•āĻ°āĻž āĻšā§Ÿā§‡āĻ›ā§‡]   〈6.1.a〉āĻŦāĻŋāĻ¨ā§āĻ¯āĻžāĻ¸ āĻ“ āĻ¸āĻŽāĻžāĻŦā§‡āĻļ Counting problems āĻāĻ° āĻāĻ•āĻŸāĻŋ āĻŽā§ŒāĻ˛āĻŋāĻ• āĻŦāĻŋāĻˇā§Ÿ āĻšāĻ˛ā§‹āĻƒ āĻāĻ•āĻŸāĻŋ āĻ˜āĻŸāĻ¨āĻž [latex]n[latex] āĻ‰āĻĒāĻžā§Ÿā§‡ āĻ•āĻ°āĻžāĻ° āĻĒāĻ°ā§‡ āĻĻā§āĻŦāĻŋāĻ¤ā§€ā§Ÿ āĻ†āĻ°ā§‡āĻ•āĻŸāĻŋ āĻ˜āĻŸāĻ¨āĻž āĻ¯āĻĻāĻŋ [latex]m[latex] āĻ‰āĻĒāĻžā§Ÿā§‡ āĻ•āĻ°āĻž āĻ¯āĻžā§Ÿ, āĻ¤āĻžāĻšāĻ˛ā§‡ āĻĻā§āĻ‡āĻŸāĻŋ āĻ˜āĻŸāĻ¨āĻž āĻāĻ•āĻ¸āĻžāĻĨā§‡ [latex]mn[latex] āĻ‰āĻĒāĻžā§Ÿā§‡ āĻ˜āĻŸāĻžāĻ¨ā§‹ āĻ¯āĻžā§ŸāĨ¤ āĻ•āĻŋāĻ›ā§ āĻ‰āĻĻāĻžāĻšāĻ°āĻŖ āĻĻā§‡āĻ–ā§āĻ¨āĻƒ […]

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