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