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Permutation and CombinationQuestion and Answers: Page 15

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Find the number of six−digit odd numbers without repeated digits.

$${Find}\:{the}\:{number}\:{of}\:{six}−{digit}\:{odd} \\ $$$${numbers}\:{without}\:{repeated}\:{digits}. \\ $$

Question Number 101732 Answers: 2 Comments: 1

There are 10 identical mathematics books, 7 identical physics books and 5 identical chemistry books. Find the number of ways to compile the books under the condition that same books are not mutually adjacent.

$$\mathrm{There}\:\mathrm{are}\:\mathrm{10}\:\mathrm{identical}\:\mathrm{mathematics} \\ $$$$\mathrm{books},\:\mathrm{7}\:\mathrm{identical}\:\mathrm{physics}\:\mathrm{books} \\ $$$$\mathrm{and}\:\mathrm{5}\:\mathrm{identical}\:\mathrm{chemistry}\:\mathrm{books}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{ways}\:\mathrm{to}\:\mathrm{compile}\: \\ $$$$\mathrm{the}\:\mathrm{books}\:\mathrm{under}\:\mathrm{the}\:\mathrm{condition}\:\mathrm{that} \\ $$$$\mathrm{same}\:\mathrm{books}\:\mathrm{are}\:\mathrm{not}\:\mathrm{mutually}\:\mathrm{adjacent}. \\ $$

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A woman sent 8 letters to her friends. The letters are kept in the addressed envelopes at random. The probability that 4 friends receive correct letters and 4 letters go to wrong destination, is ___

$$\mathrm{A}\:\mathrm{woman}\:\mathrm{sent}\:\mathrm{8}\:\mathrm{letters}\:\mathrm{to}\:\mathrm{her}\: \\ $$$$\mathrm{friends}.\:\mathrm{The}\:\mathrm{letters}\:\mathrm{are}\:\mathrm{kept}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{addressed}\:\mathrm{envelopes}\:\mathrm{at}\:\mathrm{random}.\: \\ $$$$\mathrm{The}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{4}\:\mathrm{friends}\: \\ $$$$\mathrm{receive}\:\mathrm{correct}\:\mathrm{letters}\:\mathrm{and}\:\mathrm{4}\:\mathrm{letters}\: \\ $$$$\mathrm{go}\:\mathrm{to}\:\mathrm{wrong}\:\mathrm{destination},\:\mathrm{is}\:\_\_\_\: \\ $$

Question Number 100444 Answers: 4 Comments: 0

Find the number of five−digit numbers containing exactly three different digits? Examples: 12312, 12224

$${Find}\:{the}\:{number}\:{of}\:{five}−{digit}\:{numbers} \\ $$$${containing}\:{exactly}\:{three}\:{different} \\ $$$${digits}?\:{Examples}:\:\mathrm{12312},\:\mathrm{12224} \\ $$

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A certain wire has length 4.5 cm and mass 12.3 g, with an electrical resistance of 1.1 mΩ. this wire falls through a horizontal magnetic field with flux density of 0.35 T. As his wire falls its ends slide smoothly between two rails connected by a wire with negligible internal resistance. Calculate the magnitude of the terminal energy resistance, neglecting the resistance of the rails.

$$\mathrm{A}\:\mathrm{certain}\:\mathrm{wire}\:\mathrm{has}\:\mathrm{length}\:\mathrm{4}.\mathrm{5}\:\mathrm{cm}\:\mathrm{and}\:\mathrm{mass}\:\mathrm{12}.\mathrm{3}\:\mathrm{g},\:\:\mathrm{with}\:\mathrm{an} \\ $$$$\mathrm{electrical}\:\mathrm{resistance}\:\mathrm{of}\:\mathrm{1}.\mathrm{1}\:\mathrm{m}\Omega.\:\mathrm{this}\:\mathrm{wire}\:\mathrm{falls}\:\mathrm{through}\:\mathrm{a}\:\mathrm{horizontal} \\ $$$$\mathrm{magnetic}\:\mathrm{field}\:\:\mathrm{with}\:\mathrm{flux}\:\mathrm{density}\:\mathrm{of}\:\mathrm{0}.\mathrm{35}\:\mathrm{T}.\:\mathrm{As}\:\mathrm{his}\:\mathrm{wire}\:\mathrm{falls}\:\mathrm{its}\:\mathrm{ends} \\ $$$$\mathrm{slide}\:\mathrm{smoothly}\:\mathrm{between}\:\mathrm{two}\:\mathrm{rails}\:\mathrm{connected}\:\mathrm{by}\:\mathrm{a}\:\mathrm{wire}\:\mathrm{with}\:\mathrm{negligible} \\ $$$$\mathrm{internal}\:\mathrm{resistance}.\:\mathrm{Calculate}\:\mathrm{the}\:\mathrm{magnitude}\:\mathrm{of}\:\mathrm{the}\:\mathrm{terminal}\:\mathrm{energy} \\ $$$$\mathrm{resistance},\:\mathrm{neglecting}\:\mathrm{the}\:\mathrm{resistance}\:\mathrm{of}\:\mathrm{the}\:\mathrm{rails}. \\ $$

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NB:P(E) means a set of all part of E

$$\boldsymbol{{NB}}:\boldsymbol{\mathcal{P}}\left(\boldsymbol{\mathrm{E}}\right)\:\mathrm{means}\:\mathrm{a}\:\mathrm{set}\:\mathrm{of}\:\mathrm{all}\:\mathrm{part}\:\mathrm{of}\:\boldsymbol{\mathrm{E}} \\ $$

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One card is randomly selected from a pack of 52 playing cards. Determine the probability that is a picture card.

$$\mathrm{One}\:\mathrm{card}\:\mathrm{is}\:\mathrm{randomly}\:\mathrm{selected} \\ $$$$\mathrm{from}\:\mathrm{a}\:\mathrm{pack}\:\mathrm{of}\:\mathrm{52}\:\mathrm{playing}\:\mathrm{cards}. \\ $$$$\mathrm{Determine}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that}\: \\ $$$$\mathrm{is}\:\mathrm{a}\:\mathrm{picture}\:\mathrm{card}.\: \\ $$

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a committee consisting of 5 men & 4 women is to be chosen from 8 men & 4 women. If one man & one woman are husband & wife , how many ways can the committee be chosen if only one of the husband & wife must be chosen ?

$$\mathrm{a}\:\mathrm{committee}\:\mathrm{consisting}\:\mathrm{of} \\ $$$$\mathrm{5}\:\mathrm{men}\:\&\:\mathrm{4}\:\mathrm{women}\:\mathrm{is}\:\mathrm{to}\:\mathrm{be}\: \\ $$$$\mathrm{chosen}\:\mathrm{from}\:\mathrm{8}\:\mathrm{men}\:\&\:\mathrm{4}\:\mathrm{women}. \\ $$$$\mathrm{If}\:\mathrm{one}\:\mathrm{man}\:\&\:\mathrm{one}\:\mathrm{woman}\:\mathrm{are}\:\mathrm{husband}\: \\ $$$$\&\:\mathrm{wife}\:,\:\mathrm{how}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{can}\: \\ $$$$\mathrm{the}\:\mathrm{committee}\:\mathrm{be}\:\mathrm{chosen}\:\mathrm{if} \\ $$$$\mathrm{only}\:\mathrm{one}\:\mathrm{of}\:\mathrm{the}\:\mathrm{husband}\:\&\:\mathrm{wife} \\ $$$$\mathrm{must}\:\mathrm{be}\:\mathrm{chosen}\:? \\ $$

Question Number 96815 Answers: 1 Comments: 0

In how many ways can 3 boys and 3 girls be sitted in a line?

$$\mathrm{In}\:\mathrm{how}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{3}\:\mathrm{boys}\:\mathrm{and}\:\mathrm{3}\:\mathrm{girls}\:\mathrm{be} \\ $$$$\mathrm{sitted}\:\mathrm{in}\:\mathrm{a}\:\mathrm{line}? \\ $$

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