3. (16pts) Answer the following questions: a) (4pts) In the general education co

Question

3. (16pts) Answer the following questions: a) (4pts) In the general education course requirement at a college, a student need to choose one each from social sciences, humanities, natural sciences, and foreign languages There are 5 social science courses, 6 humanity courses, 3 natural science courses, and 4 foreign language courses available for general education. How many different ways can a student choose general education courses from these four areas? b) (4pts) 4 people are chosen from a 25-member club for president, vice president, secretary, and treasurer. In how many different ways can this be done? c) (4pts) A student is randomly choosing the answer to each of 5 true-false questions in a test. How many possible ways can the student answer the five questions? d) (4pts) In a poker game, how many possible ways can a hand of 7 cards be dealt?

Explanation / Answer

a) here number of ways =N(choose 1 from 5 social sicence; 1 from 6 humnaity coursse; 1 from 3 natural science and 1 from 4 foreign language) =5*6*3*4= 360

b)

as we need to select 4 and than arrange them in their respective position; hence

number of ways =25P4 =25!/(25-4)! =25*24*23*22=303600

c)

here as each question can be answered in 2 ways; therefore number of ways =2*2*2*2*2 =32

d)

number of ways =N(chosinig 7 cards from 52) =52C7 =52!/(7!*(52-7)!)=133784560

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