Question

In a survey of​ four-year colleges and​ universities, it was found that 255 offered a liberal arts degree. 110 offered a computer engineering degree. 481 offered a nursing degree. 30 offered a liberal arts degree and a computer engineering degree. 211 offered a liberal arts degree and a nursing degree. 86 offered a computer engineering degree and a nursing degree. 25 offered a liberal arts​ degree, a computer engineering​ degree, and a nursing degree. 33 offered none of these degrees.

A.  How many​ four-year colleges and universities were​ surveyed? There were ___​four-year colleges and universities surveyed. Of the​ four-year colleges and universities​ surveyed, how many offered

B.  a liberal arts degree and a nursing​ degree, but not a computer engineering ​degree? There are ____ ​four-year colleges and universities that offer a liberal arts degree and a nursing​ degree, but not a computer engineering degree.

C.  a computer engineering ​degree, but neither a liberal arts degree nor a nursing​ degree? There are ____ ​four-year colleges and universities that offer a computer engineering ​degree, but neither a liberal arts degree nor a nursing degree.

D.  a liberal arts​ degree, a computer engineering​ degree, and a nursing​ degree? There are ____ ​four-year colleges and universities that offer a liberal arts​ degree, a computer engineering​ degree, and a nursing degree. Enter your answer in each of the answer boxes.

Answer 1

Answer:

a)

To give the required terms

Consider,

Number of colleges or universities who offered at least one degree = arts + computer engineering + nursing - arts and computer engineering - arts and nursing - computer engineering and nursing + all three

substitute the given values in above formula

= 255 + 110 + 481 - 30 - 211 - 86 + 25

Number of colleges or universities who offered at least one degree = 544

Number of colleges or universities surveyed = Number of colleges or universities who offered + Number of colleges or universities who don't offered

substitute the given values

= 544 + 33

Number of colleges or universities surveyed = 577

Of the four year colleges and universities surveyed, 544 offered.

b)

Here arts and nursing but not computer engineering = arts and nursing - all three

substitute given values

= 211 - 25

The arts and nursing but not computer engineering = 186

c)

Only computer engineering = computer engineering - arts and computer engineering - nursing and computer engineering + all three

substitute given values

= 110 - 30 - 86 + 25

Only computer engineering = 19

d)

Here arts, nursing and computer engineering together = 25