Answer the following questions. a. in the general education course requirement at a college, a student needs to choose one each from social sciences, humanities, natural sciences, and foreign languages. there are 5 social science courses, 4 humanity courses, 4 natural science courses, and 3 foreign language courses available for general education.

a. how many different ways can a student choose general education courses from these 4 areas?
b. four 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. in how many different ways can 5 tosses of a coin yield 2 heads and 3 tails?

a) N = 240 ways

b) N = 303,600 ways

c) N = 10 ways

Step-by-step explanation:

a) Given

General course consist of one course from each of 4 groups.

Social Science = 5 options

Humanities = 4 options

Natural sciences = 4 options

Foreign language = 3 options.

Therefore the total number of possible ways of selecting one each from each of the 4 groups is:

N = 5×4×4×3 = 240 ways

b) if four people are chosen from 25 member for four different positions, that makes it a permutation problem because order of selection is important.

N = nPr = n!/(n-r)!

n = 25 and r = 4

N = 25P4 = 25!/(25-4)! = 25!/21!

N = 303,600 ways

c) The number of ways by which 5 tosses of coin can yield 2 heads and 3 tails.

N = 5!/(5-5)!(2!)(3!)

N = 5×4/2

N = 10 ways

1; 35 is the ratio

step-by-step explanation:

d. 24+-0.114

step-by-step explanation:

the question requires us to calculate the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle in the sample given the following statistics;

sample mean = 24

standard deviation, σ = 0.4

sample size , n = 49

the confidence interval for a population mean is calculated using the formula;

sample mean ± z-score*(σ/sqrt(n))

the z-score associated with a 95% confidence interval, from the standard normal tables, is;

1.96

substituting these values into the formula;

24 ± 1.96*(0.4/7)

= 24 ± 0.112

from the alternatives given, choice d is closest to the above expression;